{"id":6565,"date":"2025-12-24T17:21:06","date_gmt":"2025-12-24T08:21:06","guid":{"rendered":"https:\/\/math-travel.com\/?p=6565"},"modified":"2026-02-11T17:22:52","modified_gmt":"2026-02-11T08:22:52","slug":"taisuu-kihon","status":"publish","type":"post","link":"https:\/\/math-travel.jp\/math-2\/taisuu-kihon\/","title":{"rendered":"\u5bfe\u6570(log)\u3068\u306f\uff1f\u610f\u5473\u3068\u57fa\u672c\u516c\u5f0f8\u9078\u3010\u521d\u5fc3\u8005\u3067\u3082\u308f\u304b\u308b\u8a08\u7b97\u306e\u30eb\u30fc\u30eb\u3011"},"content":{"rendered":"\n

\u300c\u5bfe\u6570\u3063\u3066\u306a\u306b\uff1f\u300d<\/span>
\u300c\u6307\u6570\u3068log\u306e\u95a2\u4fc2\u304c\u5206\u304b\u3089\u306a\u3044\u300d<\/span>
\u4eca\u56de\u306f\u5bfe\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

log\u3067\u8868\u3059\u306e\u304c\u82e6\u624b\u3067\u3059\u2026<\/p>\n<\/span><\/span><\/span><\/div><\/div><\/div><\/div>\n\n\n

\u5bfe\u6570\u306b\u82e6\u624b\u610f\u8b58\u304c\u3042\u308b\u65b9\u3063\u3066\u591a\u3044\u3067\u3059\u3088\u306d…<\/p>\n\n\n\n

\u307c\u304f\u81ea\u8eab\u3001\u5b66\u751f\u6642\u4ee3\u306f\u5bfe\u6570\u304c\u82e6\u624b\u3060\u3063\u305f\u899a\u3048\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n\n\n\n

\u5bfe\u6570\u3092\u4f7f\u3046\u3053\u3068\u3067\u3001\u975e\u5e38\u306b\u3081\u3093\u3069\u3046\u306a\u8a08\u7b97\u3092\u30b9\u30de\u30fc\u30c8\u306b\u8a08\u7b97\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u305f\u308a\u3057\u307e\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

\u672c\u8a18\u4e8b\u3067\u306f\u5bfe\u6570log\u306e\u610f\u5473\u3068\u91cd\u8981\u306a\u516c\u5f0f<\/span>\u306b\u3064\u3044\u3066\u89e3\u8aac\u3057\u307e\u3059\u3002<\/p>\n\n\n\n

\u3053\u306e\u8a18\u4e8b\u3092\u8aad\u3081\u3070\u3001\u5bfe\u6570\u306e\u610f\u5473\u3084\u57fa\u672c\u306e\u8a08\u7b97\u306b\u3064\u3044\u3066\u7406\u89e3\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n

\u3053\u3053\u3089\u8fba\u306f\u30d5\u30ef\u30c3\u3068\u7406\u89e3\u3057\u3066\u3044\u308b\u65b9\u304c\u591a\u3044\u306e\u3067\u3001\u3057\u3063\u304b\u308a\u7406\u89e3\u3057\u3066\u5dee\u3092\u4ed8\u3051\u307e\u3057\u3087\u3046\u3002<\/p>\n\n\n

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

\u6c17\u306b\u306a\u308b\u898b\u51fa\u3057\u3092\u30af\u30ea\u30c3\u30af\u3057\u3066\u3001
\u305c\u3072\u6700\u5f8c\u307e\u3067\u3054\u89a7\u304f\u3060\u3055\u3044<\/p>\n<\/span><\/span><\/span><\/div><\/div><\/div><\/div>\n\n\n

\u5bfe\u6570\u3068\u306f\uff1flog\u306e\u610f\u5473<\/h2>\n\n\n\n

\u5bfe\u6570\\(log_{a}M\\)\u3068\u306f\u3001\u300c\\(M\\)\u306f\\(a\\)\u306e\u4f55\u4e57\u306a\u306e\u304b\u300d<\/span>\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

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

\u5bfe\u6570log\u306e\u4f8b<\/h3>\n\n\n\n

2\u306e3\u4e57\u306f8\u3067\u3059\u3088\u306d\u3002<\/p>\n\n\n\n

\\[2^{3}=8\\]<\/p>\n\n\n\n

\u3053\u308c\u3092\u5bfe\u6570\u3092\u4f7f\u3063\u3066\u8868\u3059\u3068\u3001<\/p>\n\n\n\n

\\[log_{2}8=3\\]<\/p>\n\n\n\n

\u3068\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n

\\[2^{3}=8 \\Leftrightarrow log_{2}8=3\\]<\/p>\n\n\n\n

\u3053\u308c\u3089\u306f\u6307\u6570\u3067\u8868\u3059\u304b\u3001\u5bfe\u6570\u3067\u8868\u3059\u304b\u306e\u9055\u3044\u3067\u3059\u3002<\/p>\n\n\n\n

\u96e3\u3057\u304f\u8003\u3048\u3059\u304e\u306a\u3044\u307b\u3046\u304c\u3001\u30b9\u30e0\u30fc\u30ba\u306b\u7406\u89e3\u3067\u304d\u308b\u3067\u3057\u3087\u3046\u3002<\/p>\n\n\n

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

\u5e95a\u306e\u4f55\u4e57\u306a\u306e\u304b\u3092\u8868\u3057\u3066\u3044\u308b\u3093\u3067\u3059\u306d<\/p>\n<\/span><\/span><\/span><\/div><\/div><\/div><\/div>\n\n\n

\u5e95\u3068\u771f\u6570\u304c\u8868\u3059\u3082\u306e<\/h2>\n\n\n\n

\\(log_{a}b=x\\)\u306b\u304a\u3051\u308b\\(a\\)\u3092\u5e95\uff08\u3066\u3044\uff09<\/span>\u3001\\(b\\)\u3092\u771f\u6570\uff08\u3057\u3093\u3059\u3046\uff09<\/span>\u3068\u3044\u3044\u307e\u3059\u3002<\/p>\n\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<\/span>\u3001\\(x\\)\u3092\u6307\u6570<\/span>\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

\u771f\u6570\u6761\u4ef6<\/h3>\n\n\n\n

\u5bfe\u6570\\(log_{a}b=x\\)\u306b\u304a\u3051\u308b\u771f\u6570\\(b\\)\u306f\u6b63\u306e\u5024\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n

\u3053\u306e\u6761\u4ef6\u306e\u3053\u3068\u3092\u771f\u6570\u6761\u4ef6<\/span>\u3068\u3044\u3044\u307e\u3059\u3002<\/p>\n\n\n

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

\u306a\u305c\u771f\u6570\u304c\u6b63\u306e\u5024\u306b\u306a\u308b\u306e\u304b\u306f\u5225\u306e\u8a18\u4e8b\u3067\u89e3\u8aac\u3057\u3066\u3044\u307e\u3059\u3002<\/p>\n\n\n

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

\u771f\u6570\u306f\u5fc5\u305a\u6b63\u306e\u5024\u306a\u3093\u3067\u3059\u306d<\/p>\n<\/span><\/span><\/span><\/div><\/div><\/div><\/div>\n\n

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

\u5f0f\u5909\u5f62\u3084\u8a3c\u660e\u3067\u51fa\u3066\u304f\u308b\u304b\u3089\u899a\u3048\u3066\u304a\u3053\u3046<\/p>\n<\/span><\/span><\/span><\/div><\/div><\/div><\/div>\n\n\n

\u5bfe\u6570\u306e\u91cd\u8981\u306a\u516c\u5f0f<\/h2>\n\n\n\n

\u5bfe\u6570\u306b\u306f\u91cd\u8981\u306a\u516c\u5f0f<\/span>\u304c\u3044\u304f\u3064\u304b\u3042\u308a\u307e\u3059\u3002<\/p>\n\n\n\n

\u5bfe\u6570\u306e\u91cd\u8981\u516c\u5f0f<\/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<\/div><\/div>\n\n\n\n

\u3053\u308c\u3089\u306f\u5bfe\u6570\u306e\u8d85\u57fa\u672c\u306e\u516c\u5f0f\u3067\u3059\u3002<\/span><\/p>\n\n\n\n

\u3053\u306e\u4ed6\u306b\u3082\u91cd\u8981\u306a\u516c\u5f0f\u304c\u3044\u304f\u3064\u3082\u3042\u308b\u306e\u3067\u3001\u3053\u3061\u3089\u306e\u8a18\u4e8b\u3082\u5408\u308f\u305b\u3066\u3054\u89a7\u304f\u3060\u3055\u3044\u3002<\/p>\n\n\n\n

\u57fa\u672c\u516c\u5f0f\u306e\u4f8b\u984c<\/h3>\n\n\n\n

\u5bfe\u6570\u306e\u57fa\u672c\u7684\u306a\u516c\u5f0f\u3092\u3064\u304b\u3063\u305f\u7df4\u7fd2\u554f\u984c\u3092\u89e3\u3044\u3066\u307f\u307e\u3057\u3087\u3046\u3002<\/p>\n\n\n\n

\u4f8b\u984c<\/span><\/div>
\n

\u6b21\u306e\u8a08\u7b97\u3092\u3057\u3066\u307f\u307e\u3057\u3087\u3046\u3002<\/p>\n\n\n\n

(1) \\(log_{3}9\\)<\/p>\n\n\n\n

(2) \\(log_{2}25\\)<\/p>\n<\/div><\/div>\n\n\n\n

(1)\u306f\u3059\u3050\u306b\u89e3\u3051\u308b\u3088\u3046\u306b\u3057\u3066\u304a\u304d\u307e\u3057\u3087\u3046\u3002<\/p>\n\n\n\n

\\begin{eqnarray}
log_{3}9&=&log_{3}3^{2}\\\\
&=&2
\\end{eqnarray}<\/p>\n\n\n\n

(2)\u306f\u6700\u5f8c\u307e\u3067log\u304c\u6b8b\u308b\u305f\u3081\u5c11\u3057\u4e0d\u5b89\u3067\u3059\u304c\u3001\u3053\u308c\u3067\u5927\u4e08\u592b\u3067\u3059\u3002<\/p>\n\n\n\n

\\begin{eqnarray}
log_{2}25&=&log_{2}5^{2}\\\\
&=&2log_{2}5
\\end{eqnarray}<\/p>\n\n\n

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

\u3053\u306e\u5f0f\u5909\u5f62\u306f\u30b9\u30e0\u30fc\u30ba\u306b\u3067\u304d\u308b\u3088\u3046\u306b\u3057\u3088\u3046<\/p>\n<\/span><\/span><\/span><\/div><\/div><\/div><\/div>\n\n

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

\u554f\u984c\u3092\u89e3\u3044\u3066\u7279\u8a13\u3057\u3066\u304a\u304d\u307e\u3059\uff01<\/p>\n<\/span><\/span><\/span><\/div><\/div><\/div><\/div>\n\n\n

\u6307\u6570\u3068\u5bfe\u6570\u306e\u95a2\u4fc2<\/h2>\n\n\n\n

\u3053\u3053\u307e\u3067\u89e3\u8aac\u3057\u305f\u3088\u3046\u306b\u3001\u6307\u6570\u3068\u5bfe\u6570\u306b\u306f\u5bc6\u63a5\u306a\u95a2\u4fc2\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n\n\n\n

\u4ee5\u4e0b\u306f\u6307\u6570\u95a2\u6570\\(y=2^{x}\\)\u306e\u30b0\u30e9\u30d5\u3067\u3059\u3002<\/p>\n\n\n

\n
\"\u6307\u6570\u95a2\u6570\\(y=2^{x}\\)\u306e\u30b0\u30e9\u30d5\"<\/figure>\n<\/div>\n\n\n

\\(x\\)\u306e\u5024\u304c\u5927\u304d\u304f\u306a\u308b\u306b\u3064\u308c\u3066\u3001\\(y\\)\u304c\u5927\u304d\u304f\u306a\u3063\u3066\u3044\u308b\u3053\u3068\u304c\u5206\u304b\u308a\u307e\u3059\u3002<\/p>\n\n\n\n

\u5e95a>1\u306e\u6307\u6570\u95a2\u6570<\/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

    \u4e00\u65b9\u3067\u3001\u5bfe\u6570\u95a2\u6570\\(y=log_{2}x\\)\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306a\u30b0\u30e9\u30d5\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n

    \n
    \"\u5bfe\u6570\u306e\u30b0\u30e9\u30d51\"<\/figure>\n<\/div>\n\n\n

    \u3069\u3093\u306a\u5bfe\u6570\u95a2\u6570\u3067\u3082\\(log_{a}1=0\\)\u306a\u306e\u3067\u3001\u70b9(1,0)\u3092\u901a\u904e\u3057\u307e\u3059\u3002<\/p>\n\n\n\n

    \\(y=2^{x}\\)\u3068\\(y=log_{2}x\\)\u306f\u3069\u3061\u3089\u3082\u5e95\u304c2\u306e\u95a2\u6570\u3067\u3059\u3002<\/p>\n\n\n\n

    \u5e95\u304c\u7b49\u3057\u3044\u6307\u6570\u95a2\u6570\u3068\u5bfe\u6570\u95a2\u6570\u306e\u30b0\u30e9\u30d5\u3092\u66f8\u304f\u3068\u3001\\(y=x\\)\u306b\u5bfe\u3057\u3066\u5bfe\u79f0\u3067\u3042\u308b\u3053\u3068\u304c\u5206\u304b\u308a\u307e\u3059\u3002<\/span><\/p>\n\n\n

    \n
    \"\u6307\u6570\u95a2\u6570\u3068\u5bfe\u6570\u95a2\u6570\"<\/figure>\n<\/div>\n\n\n

    \u305d\u3053\u307e\u3067\u91cd\u8981\u306a\u3053\u3068\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u304c\u3001\u77e5\u3063\u3066\u304a\u3044\u3066\u640d\u306f\u306a\u3044\u3067\u3057\u3087\u3046\u3002<\/p>\n\n\n

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

    \u6307\u6570\u3068\u5bfe\u6570\u304c\u9023\u52d5\u3057\u3066\u3044\u308b\u3053\u3068\u304c\u5206\u304b\u308b\u306d<\/p>\n<\/span><\/span><\/span><\/div><\/div><\/div><\/div>\n\n\n

    \u6307\u6570\u30fb\u5bfe\u6570\u306e\u7df4\u7fd2\u554f\u984c<\/h2>\n\n\n\n

    \u6307\u6570\u304b\u3089\u5bfe\u6570\u3001\u305d\u306e\u9006\u306b\u5bfe\u6570\u304b\u3089\u6307\u6570\u3078\u5f0f\u5909\u5f62\u304c\u3067\u304d\u308b\u3088\u3046\u306b\u7df4\u7fd2\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n\n\n\n

    \u7df4\u7fd2\u554f\u984c<\/span><\/div>
    \n

    \u6307\u6570\u306f\u5bfe\u6570\u306b\u3001\u5bfe\u6570\u306f\u6307\u6570\u306b\u5909\u63db\u3057\u3066\u307f\u3088\u3046\u3002<\/p>\n\n\n\n

    (1) \\(3^{3}=27\\)<\/p>\n\n\n\n

    (2) \\(log_{2}x=8\\)<\/p>\n<\/div><\/div>\n\n\n\n

    (1)\u3000\\(3^{3}=27\\)\u304b\u3089\u3000\\(log_{3}27=3\\)<\/p>\n\n\n\n

    (2)\u3000\\(log_{2}256=8\\)\u304b\u3089\u3000\\(2^{8}=256\\)<\/p>\n\n\n

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

    \u3044\u307e\u306f\u5206\u304b\u308b\u3051\u3069\u3001\u307e\u305f\u5fd8\u308c\u3061\u3083\u3044\u305d\u3046\u3067\u3059<\/p>\n<\/span><\/span><\/span><\/div><\/div><\/div><\/div>\n\n

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

    \u3053\u308c\u306f\u6163\u308c\u3066\u3044\u304f\u3057\u304b\u306a\u3044\u306d<\/p>\n<\/span><\/span><\/span><\/div><\/div><\/div><\/div>\n\n\n

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