{"id":6455,"date":"2025-12-24T17:21:06","date_gmt":"2025-12-24T08:21:06","guid":{"rendered":"https:\/\/math-travel.com\/?p=6455"},"modified":"2026-02-11T17:21:11","modified_gmt":"2026-02-11T08:21:11","slug":"shisuu-log","status":"publish","type":"post","link":"https:\/\/math-travel.jp\/math-2\/shisuu-log\/","title":{"rendered":"\u3010\u6307\u6570\u30fb\u5bfe\u6570\u95a2\u6570\u3011log\u306e\u516c\u5f0f\u30fb\u6027\u8cea\u3092\u7dcf\u307e\u3068\u3081\uff01\u8a08\u7b97\u3092\u5b8c\u74a7\u306b\u3059\u308b\u5fb9\u5e95\u89e3\u8aac"},"content":{"rendered":"\n

\u300c\u6307\u6570\u95a2\u6570\u30fb\u5bfe\u6570\u95a2\u6570\u304c\u82e6\u624b\u300d<\/span>
\u300c\u6307\u6570\u30fb\u5bfe\u6570\u306e\u7dcf\u5fa9\u7fd2\u304c\u3057\u305f\u3044\u300d<\/span>
\u4eca\u56de\u306f\u6307\u6570\u95a2\u6570\u3068\u5bfe\u6570\u95a2\u6570\u306b\u95a2\u3059\u308b\u3053\u3093\u306a\u60a9\u307f\u3092\u89e3\u6c7a\u3057\u307e\u3059\u3002<\/p>\n\n\n

\"\"\u9ad8\u6821\u751f<\/span><\/div>
\n

\u30c6\u30b9\u30c8\u306b\u5411\u3051\u3066\u6307\u6570\u30fb\u5bfe\u6570\u306e\u5fa9\u7fd2\u304c\u3057\u305f\u3044\u3067\u3059\u2026<\/p>\n<\/span><\/span><\/span><\/div><\/div><\/div><\/div>\n\n\n

\u672c\u8a18\u4e8b\u3067\u306f\u6307\u6570\u30fb\u5bfe\u6570\u95a2\u6570\u306b\u3064\u3044\u3066\u5fb9\u5e95\u89e3\u8aac<\/span>\u3057\u3066\u3044\u307e\u3059\u3002<\/p>\n\n\n\n

\u305c\u3072\u5b9a\u671f\u30c6\u30b9\u30c8\u306b\u5411\u3051\u305f\u7dcf\u5fa9\u7fd2\u306b\u6d3b\u7528\u3057\u3066\u304f\u3060\u3055\u3044\u3002<\/p>\n\n\n\n

\u6307\u6570\u95a2\u6570<\/h2>\n\n\n\n

\u6307\u6570\u95a2\u6570\u3068\u306f\u3001\\(a>0,a\u22601\\)\u3068\u3057\u3066\\(y=a^{x}\\)\u306e\u3088\u3046\u306b\u6307\u6570\u306b\u5909\u6570\u3092\u542b\u3080\u95a2\u6570\u3067\u3059\u3002<\/span><\/p>\n\n\n\n

\u6307\u6570\u95a2\u6570<\/span><\/div>
\n

\\(a>0,a\u22601\\)\u306e\u3068\u304d<\/p>\n\n\n\n

\\[y=a^{x}\\]<\/p>\n<\/div><\/div>\n\n\n\n

\\(y=a^{x}\\)\u306b\u304a\u3044\u3066\u3001\\(a\\)\u306e\u3053\u3068\u3092\u5e95\uff08\u3066\u3044<\/span>\uff09\u3068\u3044\u3044\u3001\\(x\\)\u306e\u3053\u3068\u3092\u6307\u6570\uff08\u3057\u3059\u3046\uff09<\/span>\u3068\u547c\u3073\u307e\u3059\u3002<\/p>\n\n\n

\n
\"\u5e95\u3068\u771f\u6570\u304c\u8868\u3059\u3082\u306e\"<\/figure>\n<\/div>\n\n\n

\u3064\u307e\u308a\u3001\\(y=a^{x}\\)\u306f\u300c\u5e95\u304c\\(a\\),\u6307\u6570\\(x\\)\u306e\u6307\u6570\u95a2\u6570\u300d\u3068\u3044\u3046\u3053\u3068\u3067\u3059\u306d\u3002<\/p>\n\n\n\n

\u6307\u6570\u95a2\u6570\u306e\u30b0\u30e9\u30d5\u306f\u3069\u3093\u306a\u5f62\uff1f<\/h3>\n\n\n\n

\u6307\u6570\u95a2\u6570\u306e\u30b0\u30e9\u30d5\u3092\u30a4\u30e1\u30fc\u30b8\u3067\u304d\u307e\u3059\u304b\uff1f<\/p>\n\n\n\n

\u5e95\u306e\u5024\u306b\u3088\u3063\u3066\u3001\u6307\u6570\u95a2\u6570\u306e\u30b0\u30e9\u30d5\u306f\u5909\u5316\u3059\u308b\u306e\u3067\u6ce8\u610f\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n\n\n\n

[1] \\(a>1\\)\u306e\u3068\u304d<\/p>\n\n\n

\n
\"\u6307\u6570\u95a2\u6570\u306e\u30b0\u30e9\u30d5\"<\/figure>\n<\/div>\n\n\n
a>1\u306e\u3068\u304d<\/span><\/div>
\n
    \n
  • \u70b9\\((0,1)\\)\u3092\u901a\u308b<\/li>\n\n\n\n
  • \\(x\\)\u304c\u5927\u304d\u304f\u306a\u308b\u307b\u3069\u5897\u52a0<\/li>\n\n\n\n
  • \\(x\\)\u304c\u5c0f\u3055\u304f\u306a\u308b\u307b\u30690\u306b\u8fd1\u3065\u304f<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n

    [2] \\(a<1\\)\u306e\u3068\u304d<\/p>\n\n\n

    \n
    \"\u6307\u6570\u306e\u5e95\u304c1\u3088\u308a\u5c0f\u3055\u3044\u3068\u304d\"<\/figure>\n<\/div>\n\n\n
    a<1\u306e\u3068\u304d<\/span><\/div>
    \n
      \n
    • \u70b9\\((0,1)\\)\u3092\u901a\u308b<\/li>\n\n\n\n
    • \\(x\\)\u304c\u5927\u304d\u304f\u306a\u308b\u307b\u30690\u306b\u8fd1\u3065\u304f<\/li>\n\n\n\n
    • \\(x\\)\u304c\u5c0f\u3055\u304f\u306a\u308b\u307b\u3069\u5897\u52a0<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n

      \u6307\u6570\u95a2\u6570\u306e\u30b0\u30e9\u30d5\u306e\u66f8\u304d\u65b9\u306f\u3053\u3061\u3089\u3067\u307e\u3068\u3081\u307e\u3057\u305f\u3002<\/p>\n\n\n\n

      \u21d2\u5bfe\u6570\u95a2\u6570\u306e\u30b0\u30e9\u30d5\u3068\u66f8\u304d\u65b93\u30b9\u30c6\u30c3\u30d7\u3092\u89e3\u8aac\uff01<\/p>\n\n\n\n

      \u6307\u6570\u306e\u8a08\u7b97\u516c\u5f0f<\/h3>\n\n\n\n

      \u6307\u6570\u95a2\u6570\u3092\u4f7f\u3044\u3053\u306a\u3059\u306b\u306f\u6307\u6570\u6cd5\u5247<\/span>\u306e\u7406\u89e3\u3082\u6b20\u304b\u305b\u307e\u305b\u3093\u3002<\/p>\n\n\n\n

      \u4ee5\u4e0b\u304c\u6307\u6570\u6cd5\u5247\u306e\u91cd\u8981\u306a\u516c\u5f0f\u3067\u3059\u3002<\/span><\/p>\n\n\n\n

      \u6307\u6570\u6cd5\u5247\u306e\u57fa\u672c\u516c\u5f0f<\/span><\/div>
      \n
        \n
      • \\(a\u22600,b\u22600\\)\u3067\u3001\\(m,n\\)\u304c\u6574\u6570\u306e\u3068\u304d<\/li>\n\n\n\n
      • \\(a^{m} \\times a^{n}=a^{m+n}\\)<\/li>\n\n\n\n
      • \\((a^{m})^{n}=a^{mn}\\)<\/li>\n\n\n\n
      • \\((ab)^{n}=a^{n}b^{n}\\)<\/li>\n\n\n\n
      • \\(a^{m} \\div a^{n}=a^{m-n}\\)<\/li>\n\n\n\n
      • \\(\\displaystyle \\left(\\frac{a}{b} \\right)^{n}=\\frac{a^{n}}{b^{n}}\\)<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n

        \u4ee5\u4e0b\u306e3\u3064\u306e\u516c\u5f0f\u3082\u304b\u306a\u308a\u91cd\u8981\u3067\u3059\u3002<\/p>\n\n\n\n

        \u6307\u6570\u6cd5\u5247\u306e\u91cd\u8981\u516c\u5f0f<\/span><\/div>
        \n

        \\(a\u22600,b\u22600\\)\u3067\u3001\\(m,n\\)\u304c\u6574\u6570\u306e\u3068\u304d<\/p>\n\n\n\n

          \n
        • \\(a^{0}=1\\)<\/li>\n\n\n\n
        • \\(\\displaystyle a^{-n}=\\frac{1}{a^{n}}\\)<\/li>\n\n\n\n
        • \\(\\displaystyle a^{\\frac{1}{n}}=\\sqrt[n]{a}\\)<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n

          \u3053\u3053\u3067\u306f\u516c\u5f0f\u306e\u7d39\u4ecb\u3057\u304b\u3057\u307e\u305b\u3093\u304c\u3001\u8a73\u3057\u3044\u4f7f\u3044\u65b9\u3084\u7df4\u7fd2\u554f\u984c\u306f\u300c\u6307\u6570\u6cd5\u5247\u306e\u91cd\u8981\u306a\u516c\u5f0f8\u9078\uff01\u3053\u308c\u3067\u5206\u6570\u3084\u30de\u30a4\u30ca\u30b9\u306b\u3082\u56f0\u3089\u306a\u3044\uff01\u300d\u3067\u89e3\u8aac\u3057\u3066\u3044\u307e\u3059\u3002<\/p>\n\n\n\n

          \u6307\u6570\u65b9\u7a0b\u5f0f<\/h3>\n\n\n\n

          \u4ee5\u4e0b\u306e\u3088\u3046\u306a\u6307\u6570\u95a2\u6570\u3092\u542b\u3080\u65b9\u7a0b\u5f0f\u3092\u6307\u6570\u65b9\u7a0b\u5f0f<\/span>\u3068\u3044\u3044\u307e\u3059\u3002<\/p>\n\n\n\n

          \u6307\u6570\u65b9\u7a0b\u5f0f\u306e\u4f8b<\/span><\/div>
          \n

          \\[2^{x}=8\\]<\/p>\n\n\n\n

          \\[9^{x}+3^{x}=90\\]<\/p>\n\n\n\n

          \\[2^{2x}-6 \\cdot 2^{x} +8=0\\]<\/p>\n<\/div><\/div>\n\n\n\n

          \u65b9\u7a0b\u5f0f\u3092\u89e3\u304f\u3068\u3044\u3046\u306e\u306f\u3001\u4e0e\u3048\u3089\u308c\u305f\u7b49\u5f0f\u3092\u6210\u308a\u7acb\u305f\u305b\u308b\\(x\\)\u306e\u5024\u3092\u6c42\u3081\u308b\u3053\u3068\u3092\u6307\u3057\u307e\u3059\u3002<\/p>\n\n\n\n

          \u6307\u6570\u65b9\u7a0b\u5f0f\u306e\u89e3\u304d\u65b9\u306b\u306f\u5927\u304d\u304f5\u3064\u30d1\u30bf\u30fc\u30f3\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n\n\n\n

          \u6307\u6570\u65b9\u7a0b\u5f0f\u306e5\u30d1\u30bf\u30fc\u30f3<\/span><\/div>
          \n
            \n
          • \u5e95\u3092\u305d\u308d\u3048\u308b\u554f\u984c<\/li>\n\n\n\n
          • \u30eb\u30fc\u30c8\u3084\u5206\u6570\u304c\u3042\u308b\u554f\u984c<\/li>\n\n\n\n
          • \u7f6e\u304d\u63db\u3048\u308b\u554f\u984c<\/li>\n\n\n\n
          • \u5bfe\u6570\u3067\u7b54\u3048\u308b\u554f\u984c<\/li>\n\n\n\n
          • \u9023\u7acb\u65b9\u7a0b\u5f0f\u306e\u554f\u984c<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n

            \u305d\u308c\u305e\u308c\u306e\u89e3\u304d\u65b9\u306f\u300c\u6307\u6570\u65b9\u7a0b\u5f0f\u306e\u89e3\u304d\u65b9\uff01\u51685\u30d1\u30bf\u30fc\u30f3\u3092\u5206\u304b\u308a\u3084\u3059\u304f\u89e3\u8aac\uff01\u300d\u306b\u3066\u89e3\u8aac\u3057\u307e\u3057\u305f\u3002<\/p>\n\n\n\n

            \u6307\u6570\u4e0d\u7b49\u5f0f<\/h3>\n\n\n\n

            \u6307\u6570\u65b9\u7a0b\u5f0f\u306e\u6b21\u306f\u6307\u6570\u4e0d\u7b49\u5f0f\u3067\u3059\u3002<\/p>\n\n\n\n

            \u4ee5\u4e0b\u306e\u3088\u3046\u306a\u6307\u6570\u306b\u5909\u6570\\(x\\)\u3092\u542b\u3080\u4e0d\u7b49\u5f0f\u3092\u6307\u6570\u4e0d\u7b49\u5f0f<\/span>\u3068\u3044\u3044\u307e\u3059\u3002<\/p>\n\n\n\n

            \n

            \\begin{eqnarray}
            2^{x}&\u2267&8\\\\
            \\displaystyle \\left(\\frac{1}{3}\\right)^{x+1}&<&\\left(\\frac{1}{9}\\right)^{x}
            \\end{eqnarray}<\/p>\n<\/div><\/div>\n\n\n\n

            \u6307\u6570\u4e0d\u7b49\u5f0f\u3092\u89e3\u304f\u3068\u304d\u306b\u306f\u5e95\\(a\\)\u306e\u5024\u306b\u6ce8\u610f<\/span>\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n\n\n\n

            \u6ce8\u610f\u30dd\u30a4\u30f3\u30c8<\/span><\/div>
            \n

            \\(a>0,a\u22601\\)\u306b\u304a\u3044\u3066<\/p>\n\n\n\n

            \\(a>1\\)\u306e\u3068\u304d\u3001\\(y=a^{x}\\)\u306f\u5897\u52a0\u95a2\u6570\u306a\u306e\u3067<\/p>\n\n\n\n

            \\[a^{m}<a^{n} \\Leftrightarrow m<n\\]<\/p>\n\n\n\n

            \\(0<a<1\\)\u306e\u3068\u304d\u3001\\(y=a^{x}\\)\u306f\u6e1b\u5c11\u95a2\u6570\u306a\u306e\u3067<\/p>\n\n\n\n

            \\[a^{m}<a^{n} \\Leftrightarrow m>n\\]<\/p>\n<\/div><\/div>\n\n\n\n

            \u6307\u6570\u4e0d\u7b49\u5f0f\u306b\u3082\u89e3\u304d\u65b9\u304c\u3042\u308a\u3001\u300c\u6307\u6570\u4e0d\u7b49\u5f0f\u306e\u89e3\u304d\u65b9\u3068\u6ce8\u610f\u70b9\uff01log\u3084\u7f6e\u304d\u63db\u3048\u554f\u984c\u3082\u89e3\u8aac\uff01\u300d\u306b\u3066\u89e3\u304d\u65b9\u3092\u8a73\u3057\u304f\u89e3\u8aac\u3057\u3066\u3044\u307e\u3059\u3002<\/p>\n\n\n\n

            \u6307\u6570\u4e0d\u7b49\u5f0f\u306e\u30d1\u30bf\u30fc\u30f3<\/span><\/div>
            \n
              \n
            • \u5e95\u304c1\u3088\u308a\u5927\u304d\u3044\u3068\u304d<\/li>\n\n\n\n
            • \u5e95\u304c1\u3088\u308a\u5c0f\u3055\u3044\u3068\u304d<\/li>\n\n\n\n
            • \u7f6e\u304d\u63db\u3048\u308b\u554f\u984c<\/li>\n\n\n\n
            • \u5bfe\u6570\u3092\u3068\u308b\u554f\u984c<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n

              \u5bfe\u6570\u95a2\u6570<\/h2>\n\n\n\n

              \\(y=log_{a}x\\)\u306e\u3088\u3046\u306a\u95a2\u6570\u3092\u3001\\(a\\)\u3092\u5e95\u3068\u3059\u308b\\(x\\)\u306e\u5bfe\u6570\u95a2\u6570<\/span>\u3068\u3044\u3044\u307e\u3059\u3002<\/p>\n\n\n\n

              \u5bfe\u6570\u95a2\u6570<\/span><\/div>
              \n

              \\(a>0,a\u22601,x>0\\)\u3068\u3059\u308b\u3068\u304d\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306a\u95a2\u6570\u3092\u5bfe\u6570\u95a2\u6570\u3068\u3044\u3046\u3002<\/p>\n\n\n\n

              \\[y=log_{a}x\\]<\/p>\n<\/div><\/div>\n\n\n\n

              \u5bfe\u6570log\u3068\u306f\uff1f<\/h3>\n\n\n\n

              \u5bfe\u6570\\(log_{a}M\\)\u3068\u306f\u3001\u300c\\(M\\)\u306f\\(a\\)\u306e\u4f55\u4e57\u306a\u306e\u304b\u300d\u3092\u8868\u3057\u305f\u3082\u306e\u3067\u3059\u3002<\/p>\n\n\n\n

              \u5bfe\u6570<\/span><\/div>
              \n

              \\(a>0,a\u22601\\)\u3067\\(M>0\\)\u306b\u304a\u3044\u3066\u3001<\/p>\n\n\n\n

              \\[log_{a}M=x \\Leftrightarrow a^{x}=M\\]<\/p>\n\n\n\n

              \u305f\u3060\u3057\u3001\u771f\u6570\\(b\\)\u306f\u6b63\u306e\u6570\u3067\u3042\u308b\u3002<\/p>\n<\/div><\/div>\n\n\n\n

              \\[a^{x}=M\\]<\/p>\n\n\n\n

              \\(a\\)\u306e\\(x\\)\u4e57\u304c\\(M\\)\u306e\u3068\u304d\u3001\u5bfe\u6570\u3067\u8868\u3059\u3053\u3068\u3067<\/p>\n\n\n\n

              \\[log_{a}M=x\\]<\/p>\n\n\n\n

              \u3068\u8868\u3055\u308c\u307e\u3059\u3002<\/p>\n\n\n

              \"\"\u30b7\u30fc\u30bf<\/span><\/div>
              \n

              \u6307\u6570\u3068\u5bfe\u6570\u306f\u5408\u308f\u305b\u3066\u7406\u89e3\u3057\u3066\u3044\u3053\u3046<\/p>\n<\/span><\/span><\/span><\/div><\/div><\/div><\/div>\n\n\n

              \\(log_{a}b=x\\)\u306b\u304a\u3051\u308b\\(a\\)\u3092\u5e95\uff08\u3066\u3044\uff09\u3001\\(b\\)\u3092\u771f\u6570\uff08\u3057\u3093\u3059\u3046\uff09\u3068\u3044\u3044\u307e\u3059\u3002<\/p>\n\n\n

              \n
              \"\u5e95\u3068\u771f\u6570\u304c\u8868\u3059\u3082\u306e\"<\/figure>\n<\/div>\n\n\n

              \u5e95\u306f\u6307\u6570\u3067\u8868\u3059\u3068\u304d\u306b\u3082\u4f7f\u3046\u7528\u8a9e\u306a\u306e\u3067\u899a\u3048\u3066\u304a\u304d\u307e\u3057\u3087\u3046\u3002<\/p>\n\n\n\n

              \u6307\u6570\\(a^{x}=b\\)\u306b\u304a\u3051\u308b\\(a\\)\u3092\u5e95\u3001\\(x\\)\u3092\u6307\u6570\u3068\u3044\u3044\u307e\u3059\u3002<\/p>\n\n\n\n

              \u5bfe\u6570\u306e\u6027\u8cea<\/h3>\n\n\n\n

              \u6307\u6570\u306b\u6307\u6570\u6cd5\u5247\u304c\u3042\u308b\u3088\u3046\u306b\u3001\u5bfe\u6570\u306b\u3082\u3044\u304f\u3064\u304b\u91cd\u8981\u306a\u6027\u8cea\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n\n\n\n

              \u5bfe\u6570\u306e\u6027\u8cea<\/span><\/div>
              \n

              \\(a>0,m>0,n>0,a\u22601\\)\u306b\u304a\u3044\u3066<\/p>\n\n\n\n

              \\(log_{a}a=1\\)<\/p>\n\n\n\n

              \\(log_{a}a^{m}=m\\)<\/p>\n\n\n\n

              \\(log_{a}b^{m}=m log_{a}b\\)<\/p>\n\n\n\n

              \\(log_{a}m+log_{a}n=log_{a}mn\\)<\/p>\n\n\n\n

              \\(\\displaystyle log_{a}m-log_{a}n=log_{a} \\frac{m}{n}\\)<\/p>\n<\/div><\/div>\n\n\n\n

              \u3053\u308c\u3089\u306e\u6027\u8cea\u306f\u5bfe\u6570\u306e\u8a08\u7b97\u3067\u5f53\u305f\u308a\u524d\u306e\u3088\u3046\u306b\u4f7f\u3044\u307e\u3059\u3002<\/p>\n\n\n\n

              \u5e95\u306e\u5909\u63db\u516c\u5f0f<\/h3>\n\n\n\n

              \u5e95\u306e\u5909\u63db\u516c\u5f0f\u306f\u5bfe\u6570log\u306e\u91cd\u8981\u306a\u516c\u5f0f\u306e1\u3064<\/span>\u3067\u3059\u3002<\/p>\n\n\n\n

              \u5e95\u306e\u5909\u63db\u516c\u5f0f<\/span><\/div>
              \n

              \\(a,b,c>0\u3001a,c\u22601\\)\u306e\u3068\u304d<\/p>\n\n\n\n

              \\[\\displaystyle log_{a}b=\\frac{log_{c}b}{log_{c}a}\\]<\/p>\n<\/div><\/div>\n\n\n\n

              \u4ee5\u4e0b\u306e\u3088\u3046\u306a\u5bfe\u6570\u306e\u8a08\u7b97\u304c\u3042\u3063\u305f\u3068\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n\n\n\n

              \n

              \u6b21\u306e\u8a08\u7b97\u3092\u6c42\u3081\u3088\u3046\u3002<\/p>\n\n\n\n

              \\[\\displaystyle log_{2}3 \\cdot log_{3}4\\]<\/p>\n<\/div><\/div>\n\n\n\n

              \u3053\u308c\u3089\u306f\u5bfe\u6570\u306e\u5e95\u304c\u7570\u306a\u308b\u306e\u3067\u3001\u3053\u306e\u307e\u307e\u3067\u306f\u7a4d\u3092\u6c42\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u305b\u3093\u3002<\/p>\n\n\n\n

              \u305d\u3053\u3067\u5e95\u306e\u5909\u63db\u516c\u5f0f\u306e\u51fa\u756a\u3067\u3059\u3002<\/p>\n\n\n\n

              \\[\\displaystyle log_{3}4=\\frac{log_{2}4}{log_{2}3}=\\frac{2}{log_{2}3}\\]<\/p>\n\n\n\n

              \u5e95\u306e\u5909\u63db\u516c\u5f0f\u3092\u4f7f\u3048\u3070\u3001\u5e95\u3092\u8a08\u7b97\u306e\u90fd\u5408\u304c\u3088\u3044\u5024\u306b\u5909\u63db\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u306e\u3067\u3059\u3002<\/p>\n\n\n\n

              \u3053\u306e\u554f\u984c\u3067\u306f\u3001\u5bfe\u6570\u306e\u5e95\u30922\u306b\u5909\u63db\u3057\u3066\u7a4d\u3092\u6c42\u3081\u307e\u3057\u3087\u3046\u3002<\/p>\n\n\n\n

              \\begin{eqnarray}
              \\displaystyle log_{2}3 \\cdot log_{3}4&=&log_{2}3 \\cdot \\frac{2}{log_{2}3}\\\\
              &=&2
              \\end{eqnarray}<\/p>\n\n\n\n

              \u3053\u306e\u3088\u3046\u306b\u5e95\u306e\u5909\u63db\u516c\u5f0f\u3092\u7528\u3044\u308b\u3053\u3068\u3067\u3001\u5bfe\u6570\u306e\u8a08\u7b97\u304c\u30b9\u30e0\u30fc\u30ba\u306b\u3067\u304d\u308b\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n

              \u975e\u5e38\u306b\u91cd\u8981\u306a\u516c\u5f0f\u306a\u306e\u3067\u5fc5\u305a\u899a\u3048\u3066\u304a\u304d\u307e\u3057\u3087\u3046\u3002<\/span><\/p>\n\n\n

              \n
              \"\u5e95\u306e\u5909\u63db\u516c\u5f0f\u306e\u899a\u3048\u65b9\"<\/figure>\n<\/div>\n\n\n

              \u5e95\u306e\u5909\u63db\u516c\u5f0f\u306b\u3064\u3044\u3066\u306f\u3001\u300c\u5e95\u306e\u5909\u63db\u516c\u5f0f\u306b\u3064\u3044\u3066\u89e3\u8aac\uff01\u8a3c\u660e\u3068\u5e95\u3092\u6c7a\u3081\u308b\u30b3\u30c4\u304c\u5206\u304b\u308b\uff01\u300d\u306b\u3066\u8a73\u3057\u304f\u89e3\u8aac\u3057\u3066\u3044\u307e\u3059\u3002<\/p>\n\n\n\n

              \u5bfe\u6570\u95a2\u6570\u306e\u30b0\u30e9\u30d5<\/h3>\n\n\n\n

              \u5bfe\u6570\u95a2\u6570\u306e\u30b0\u30e9\u30d5\u306e\u5f62\u306b\u3064\u3044\u3066\u8003\u3048\u3066\u3044\u304d\u307e\u3057\u3087\u3046\u3002<\/p>\n\n\n\n

              \u5bfe\u6570\u95a2\u6570\u3092\u30b0\u30e9\u30d5\u3067\u8868\u3059\u3068\u304d\u306f\u3001\u5e95\u306e\u5024\u306b\u6ce8\u610f<\/span>\u304c\u5fc5\u8981\u3067\u3059\u3002<\/p>\n\n\n\n

              \\(a>1\\)\u306e\u3068\u304d\u306f\u3001\u53f3\u4e0a\u304c\u308a\u306e\u30b0\u30e9\u30d5\u306b\u306a\u308a\u307e\u3059\u3002<\/span><\/span><\/p>\n\n\n

              \n
              \"\u5bfe\u6570\u95a2\u6570\u306e\u30b0\u30e9\u30d5\u306e\u5f62\"<\/figure>\n<\/div>\n\n\n

              \\(0<a<1\\)\u306e\u3068\u304d\u306f\u3001\u53f3\u4e0b\u304c\u308a\u306e\u30b0\u30e9\u30d5\u306b\u306a\u308a\u307e\u3059\u3002<\/span><\/span><\/p>\n\n\n

              \n
              \"\u5bfe\u6570\u95a2\u6570\u306e\u30b0\u30e9\u30d5\u306e\u5f62\"<\/figure>\n<\/div>\n\n
              \"\"\u9ad8\u6821\u751f<\/span><\/div>
              \n

              \u6ed1\u3089\u304b\u306a\u66f2\u7dda\u306b\u306a\u308b\u3093\u3067\u3059\u306d\uff01<\/p>\n<\/span><\/span><\/span><\/div><\/div><\/div><\/div>\n\n\n

              \u5bfe\u6570\u95a2\u6570\u306e\u30b0\u30e9\u30d5\u306e\u7279\u5fb4\u3092\u307e\u3068\u3081\u307e\u3057\u305f\u3002<\/p>\n\n\n\n

              \u5bfe\u6570\u95a2\u6570\u306e\u30b0\u30e9\u30d5\u306e\u7279\u5fb4<\/span><\/div>
              \n
                \n
              • \u70b9(1,0)\u3092\u901a\u308b<\/li>\n\n\n\n
              • a>1\u306e\u3068\u304d\u53f3\u4e0a\u304c\u308a\u3067\u3001\u70b9(a,1)\u3092\u901a\u308b<\/li>\n\n\n\n
              • 0<a<1\u306e\u3068\u304d\u53f3\u4e0b\u304c\u308a\u3067\u3001\u70b9(\\(\\displaystyle \\frac{1}{a}\\),-1)\u3092\u901a\u308b<\/li>\n\n\n\n
              • y\u8ef8\u304c\u6f38\u8fd1\u7dda<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n

                \u5bfe\u6570\u95a2\u6570\u306e\u30b0\u30e9\u30d5\u306e\u30dd\u30a4\u30f3\u30c8\u3084\u66f8\u304d\u65b9\u306f\u300c\u5bfe\u6570\u95a2\u6570\u306e\u30b0\u30e9\u30d5\u3068\u66f8\u304d\u65b93\u30b9\u30c6\u30c3\u30d7\u3092\u89e3\u8aac\uff01\u300d\u3067\u89e3\u8aac\u3057\u3066\u3044\u307e\u3059\u3002<\/p>\n\n\n\n

                \u5bfe\u6570\u95a2\u6570\u306e\u65b9\u7a0b\u5f0f<\/h3>\n\n\n\n

                \u5bfe\u6570\u95a2\u6570\u3092\u542b\u3080\u4ee5\u4e0b\u306e\u3088\u3046\u306a\u65b9\u7a0b\u5f0f\u3092\u5bfe\u6570\u65b9\u7a0b\u5f0f<\/span>\u3068\u3044\u3044\u307e\u3059\u3002<\/p>\n\n\n\n

                \n

                \\[log_{2}x=3\\]<\/p>\n\n\n\n

                \\[log_{4}x+log_{4}(x-6)=2\\]<\/p>\n<\/div><\/div>\n\n\n\n

                \u3053\u306e\u65b9\u7a0b\u5f0f\u3092\u6210\u308a\u7acb\u305f\u305b\u308b\\(x\\)\u3092\u6c42\u3081\u308b\u306e\u304c\u3001\u5bfe\u6570\u65b9\u7a0b\u5f0f\u306e\u4e3b\u306a\u554f\u984c\u3067\u3059\u3002<\/p>\n\n\n\n

                \u65b9\u7a0b\u5f0f\u304c\u9577\u304f\u306a\u308b\u3068\u96e3\u3057\u304f\u898b\u3048\u307e\u3059\u306d\u3002<\/p>\n\n\n

                \"\"\u9ad8\u6821\u751f<\/span><\/div>
                \n

                \u305d\u3046\u3067\u3059\u3002\u3053\u3046\u3044\u3046\u306e\u304c\u82e6\u624b\u306a\u3093\u3067\u3059..<\/p>\n<\/span><\/span><\/span><\/div><\/div><\/div><\/div>\n\n\n

                \u5bfe\u6570\u65b9\u7a0b\u5f0f\u3092\u89e3\u304f\u306b\u306f\u3001\u4ee5\u4e0b\u306e\u5f62\u3092\u76ee\u6307\u3057\u3066\u5f0f\u5909\u5f62\u3092\u3057\u3066\u3044\u304d\u307e\u3059\u3002<\/p>\n\n\n\n

                \u5bfe\u6570\u65b9\u7a0b\u5f0f\u306e\u89e3\u304d\u65b9<\/span><\/div>
                \n

                \\(a>0,a\u22601\\)\u3067\u3001\\(M>0,N>0\\)\u306e\u3068\u304d<\/p>\n\n\n\n

                \\[log_{a}M=log_{a}N\\]<\/p>\n\n\n\n

                \u306a\u3089\u3070<\/p>\n\n\n\n

                \\[M=N\\]<\/p>\n<\/div><\/div>\n\n\n\n

                \u3064\u307e\u308a\u3001<\/p>\n\n\n\n

                \\[log_{2}x=log_{2}5\u21d2x=5\\]<\/p>\n\n\n\n

                \u3068\u3044\u3046\u308f\u3051\u3067\u3059\u3002<\/p>\n\n\n\n

                \u3068\u306f\u3044\u3048\u3001\u3053\u3093\u306a\u7c21\u5358\u306a\u554f\u984c\u306f\u305d\u3046\u305d\u3046\u3042\u308a\u307e\u305b\u3093\u3002<\/p>\n\n\n\n

                \u3069\u3093\u306a\u5bfe\u6570\u65b9\u7a0b\u5f0f\u306e\u554f\u984c\u3067\u3082\u3001\u4ee5\u4e0b\u306e5\u30b9\u30c6\u30c3\u30d7\u3067\u89e3\u3092\u6c42\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/span><\/p>\n\n\n\n

                \u5bfe\u6570\u65b9\u7a0b\u5f0f\u306e\u89e3\u304d\u65b9<\/span><\/div>
                \n
                  \n
                1. \u771f\u6570\u6761\u4ef6\u3068\u5e95\u306e\u6761\u4ef6\u3092\u78ba\u8a8d<\/li>\n\n\n\n
                2. \u4e21\u8fba\u306e\u5e95\u3092\u540c\u3058\u306b\u3059\u308b<\/li>\n\n\n\n
                3. \u771f\u6570\u3092\u30a4\u30b3\u30fc\u30eb\u3067\u3080\u3059\u3076<\/li>\n\n\n\n
                4. \u65b9\u7a0b\u5f0f\u3092\u89e3\u304f<\/li>\n\n\n\n
                5. \u89e3\u3068\u6761\u4ef6\u3092\u78ba\u8a8d\u3057\u3066\u5b8c\u4e86<\/li>\n<\/ol>\n<\/div><\/div>\n\n\n\n

                  \u307e\u305f\u3001\u5bfe\u6570\u65b9\u7a0b\u5f0f\u306e\u554f\u984c\u306f\u4ee5\u4e0b\u306e4\u7a2e\u985e\u306b\u5206\u3051\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u3002<\/p>\n\n\n\n

                  \u5bfe\u6570\u65b9\u7a0b\u5f0f\u306e\u554f\u984c<\/span><\/div>
                  \n
                    \n
                  • \u57fa\u672c\u306e\u554f\u984c<\/li>\n\n\n\n
                  • \u5e95\u3092\u305d\u308d\u3048\u308b\u554f\u984c<\/li>\n\n\n\n
                  • \u7f6e\u304d\u63db\u3048\u308b\u554f\u984c<\/li>\n\n\n\n
                  • \u5e95\u306b\u6587\u5b57\u3092\u542b\u3080\u554f\u984c<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n

                    \u5bfe\u6570\u95a2\u6570\u306e\u4e0d\u7b49\u5f0f<\/h3>\n\n\n\n

                    \u5bfe\u6570\u95a2\u6570\u3092\u542b\u3080\u4e0d\u7b49\u5f0f\u3092\u5bfe\u6570\u4e0d\u7b49\u5f0f<\/span>\u3068\u3044\u3044\u307e\u3059\u3002<\/p>\n\n\n\n

                    \n

                    \\[log_{2}x>3\\]<\/p>\n\n\n\n

                    \\[2log_{3}(2-x)<log_{3}(x+4)\\]<\/p>\n<\/div><\/div>\n\n\n\n

                    \u3053\u306e\u4e0d\u7b49\u5f0f\u3092\u6e80\u305f\u3059\\(x\\)\u306e\u5909\u57df\u3092\u6c42\u3081\u307e\u3059\u3002<\/p>\n\n\n\n

                    \u5bfe\u6570\u4e0d\u7b49\u5f0f\u3092\u89e3\u304f\u3068\u304d\u306f\u3001\u771f\u6570\u6761\u4ef6\u3068\u5e95\\(a\\)\u306e\u5024\u306b\u6ce8\u610f\u3057\u307e\u3057\u3087\u3046\u3002<\/span><\/p>\n\n\n\n

                    \u771f\u6570\u6761\u4ef6<\/span><\/div>
                    \n

                    \\(y=log_{a}x\\)\u306b\u304a\u3044\u3066\u3001\u771f\u6570\\(x\\)\u306f\u6b63\u306e\u6570\u3067\u3042\u308b\u3002<\/p>\n<\/div><\/div>\n\n\n

                    \n
                    \"\u771f\u6570\u6761\u4ef6\"<\/figure>\n<\/div>\n\n\n

                    \\(b\\)\u306e\u90e8\u5206\u304c\u6b63\u3067\u3042\u308b\u3053\u3068\u306f\u5fc5\u305a\u78ba\u8a8d\u3059\u308b\u3088\u3046\u306b\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n\n\n\n

                    \u307e\u305f\u3001\u771f\u6570\u6761\u4ef6\u3068\u3042\u308f\u305b\u3066\u3001\u5e95\\(a\\)\u306e\u5024\u306b\u3082\u6ce8\u610f\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n\n\n\n

                    \u6ce8\u610f\u30dd\u30a4\u30f3\u30c8<\/span><\/div>
                    \n

                    \\(a>0.a\u22601,x>0\\)\u306b\u304a\u3044\u3066\u3001<\/p>\n\n\n\n

                    \\(a>1\\)\u306a\u3089\u3070\u3001\\(y=log_{a}x\\)\u306f\u5897\u52a0\u95a2\u6570\u306a\u306e\u3067<\/p>\n\n\n\n

                    \\[log_{a}m<log_{a}n \\Leftrightarrow m<n\\]<\/p>\n\n\n\n

                    \\(0<a<1\\)\u306a\u3089\u3070\u3001\\(y=log_{a}x\\)\u306f\u6e1b\u5c11\u95a2\u6570\u306a\u306e\u3067<\/p>\n\n\n\n

                    \\[log_{a}m<log_{a}n \\Leftrightarrow m>n\\]<\/p>\n<\/div><\/div>\n\n\n\n

                    \\(a>1\\)\u306e\u3068\u304d\u306f\u3001\u30b0\u30e9\u30d5\u304c\u53f3\u80a9\u4e0a\u304c\u308a\u306a\u306e\u3067\\(log_{a}m<log_{a}n\\)\u306e\u3068\u304d\u3001\\(m<n\\)\u304c\u6210\u308a\u7acb\u3061\u307e\u3059\u3002<\/p>\n\n\n

                    \n
                    \"\u5bfe\u6570\u4e0d\u7b49\u5f0f\u3092\u89e3\u304f\u3068\u304d\u306e\u6ce8\u610f\u70b9\"<\/figure>\n<\/div>\n\n\n
                    \n

                    \\(a>1\\)\u306e\u3068\u304d\u3001<\/p>\n\n\n\n

                    \\[alog_{a}m<log_{a}n \\Leftrightarrow m<n\\]<\/p>\n<\/div><\/div>\n\n\n\n

                    \u3057\u304b\u3057\u3001\\(0<a<1\\)\u306e\u3068\u304d\u306f\u30b0\u30e9\u30d5\u306e\u53f3\u80a9\u4e0b\u304c\u308a\u306b\u306a\u308b\u306e\u3067\u4e0d\u7b49\u53f7\u306e\u5411\u304d\u304c\u9006<\/span>\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n

                    \n
                    \"\u5bfe\u6570\u4e0d\u7b49\u5f0f\u3092\u89e3\u304f\u3068\u304d\u306e\u6ce8\u610f\u70b9\"<\/figure>\n<\/div>\n\n\n
                    \n

                    \\(0<a<1\\)\u306e\u3068\u304d\u3001<\/p>\n\n\n\n

                    \\[log_{a}m<log_{a}n \\Leftrightarrow m>n\\]<\/p>\n<\/div><\/div>\n\n\n\n

                    \u4e0d\u7b49\u5f0f\u3092\u89e3\u3044\u305f\u3089\u3001\\(a\\)\u306e\u5024\u3068\u4e0d\u7b49\u53f7\u306e\u5411\u304d\u3092\u30c1\u30a7\u30c3\u30af\u3057\u307e\u3057\u3087\u3046\u3002<\/span><\/p>\n\n\n\n

                    \u304b\u306a\u308a\u91cd\u8981\u306a\u3053\u3068\u306a\u306e\u3067\u3001\u5bfe\u6570\u4e0d\u7b49\u5f0f\u304c\u82e6\u624b\u306a\u65b9\u306f\u4ee5\u4e0b\u306e\u8a18\u4e8b\u3092\u5fc5\u305a\u8aad\u3080\u3088\u3046\u306b\u3057\u3066\u304f\u3060\u3055\u3044\u3002<\/span><\/p>\n\n\n\n

                    \u304a\u3059\u3059\u3081\u52d5\u753b<\/h2>\n\n\n\n

                    \u300a\u3068\u3042\u308b\u7537\u304c\u6388\u696d\u3092\u3057\u3066\u307f\u305f\u300b
                    \u3010\uff12\u6b21\u95a2\u6570\u30fb\uff12\u6b21\u65b9\u7a0b\u5f0f\u30fb\uff12\u6b21\u4e0d\u7b49\u5f0f\u3011\u518d\u751f\u30ea\u30b9\u30c8<\/p>\n\n\n\n