{"id":6516,"date":"2025-12-24T17:21:06","date_gmt":"2025-12-24T08:21:06","guid":{"rendered":"https:\/\/math-travel.com\/?p=6516"},"modified":"2026-02-11T17:21:54","modified_gmt":"2026-02-11T08:21:54","slug":"shisuu-houteishiki","status":"publish","type":"post","link":"https:\/\/math-travel.jp\/math-2\/shisuu-houteishiki\/","title":{"rendered":"\u6307\u6570\u65b9\u7a0b\u5f0f\u306e\u89e3\u304d\u65b9\uff1a\u7f6e\u304d\u63db\u3048\u30fb\u5bfe\u6570\u5229\u7528\u306a\u3069\u51685\u30d1\u30bf\u30fc\u30f3\u3092\u4f8b\u984c\u3067\u30de\u30b9\u30bf\u30fc"},"content":{"rendered":"\n
\u300c\u6307\u6570\u65b9\u7a0b\u5f0f\u306e\u89e3\u304d\u65b9\u304c\u5206\u304b\u3089\u306a\u3044\u300d<\/span> \u6307\u6570\u306e\u3042\u308b\u65b9\u7a0b\u5f0f\u304c\u82e6\u624b\u3067\u2026<\/p>\n<\/span><\/span><\/span><\/div><\/div><\/div><\/div>\n\n\n \u4ee5\u4e0b\u306e\u3088\u3046\u306a\u6307\u6570\u306b\u5909\u6570\\(x\\)\u3092\u542b\u3080\u65b9\u7a0b\u5f0f\u3092\u6307\u6570\u65b9\u7a0b\u5f0f<\/span>\u3068\u3044\u3044\u307e\u3059\u3002<\/p>\n\n\n\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 \u898b\u305f\u76ee\u304c\u96e3\u3057\u305d\u3046\u306a\u306e\u3067\u3001\u89e3\u304f\u524d\u304b\u3089\u82e6\u624b\u610f\u8b58\u304c\u6e67\u3044\u3066\u304d\u307e\u3059\u3088\u306d\u3002<\/p>\n\n\n\n \u5b9f\u306f\u6307\u6570\u65b9\u7a0b\u5f0f\u306e\u554f\u984c\u306f\u3001\u5927\u304d\u304f5\u3064\u306e\u30d1\u30bf\u30fc\u30f3<\/span>\u306b\u5206\u3051\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n \u3053\u306e5\u30d1\u30bf\u30fc\u30f3\u306e\u89e3\u304d\u65b9\u3055\u3048\u7406\u89e3\u3057\u3066\u304a\u3051\u3070\u3001\u5927\u4f53\u306e\u554f\u984c\u306f\u89e3\u3051\u308b\u3088\u3046\u306b\u306a\u308b\u3067\u3057\u3087\u3046\u3002<\/p>\n\n\n\n \u672c\u8a18\u4e8b\u3067\u306f\u6307\u6570\u6cd5\u5247\u306e\u89e3\u304d\u65b9\u51685\u30d1\u30bf\u30fc\u30f3\u3092\u89e3\u8aac<\/span>\u3057\u307e\u3059\u3002<\/p>\n\n\n\n \u4f8b\u984c\u3092\u4ea4\u3048\u306a\u304c\u3089\u89e3\u8aac\u3057\u3066\u3044\u304f\u306e\u3067\u3001\u305c\u3072\u6700\u5f8c\u307e\u3067\u3054\u89a7\u304f\u3060\u3055\u3044\u3002<\/p>\n\n\n \u6c17\u306b\u306a\u308b\u898b\u51fa\u3057\u3092\u30af\u30ea\u30c3\u30af\u3057\u3066\u3001 \u6307\u6570\u65b9\u7a0b\u5f0f\u306e\u524d\u306b\u6307\u6570\u95a2\u6570<\/span>\u306b\u3064\u3044\u3066\u78ba\u8a8d\u3057\u3066\u304a\u304d\u307e\u3057\u3087\u3046\u3002<\/p>\n\n\n\n \u6307\u6570\u95a2\u6570\u3068\u306f\u3001\\(a>0,a\u22601\\)\u306b\u304a\u3044\u3066\\(y=a^{x}\\)\u3068\u8868\u3055\u308c\u308b\u95a2\u6570\u3067\u3059\u3002<\/p>\n\n\n\n \\(a>0,a\u22601\\)\u306e\u3068\u304d<\/p>\n\n\n\n \\[y=a^{x}\\]<\/p>\n<\/div><\/div>\n\n\n\n \u4ee5\u4e0b\u306f\\(a>1\\)\u306b\u304a\u3051\u308b\u6307\u6570\u95a2\u6570\\(y=a^{x}\\)\u306e\u30b0\u30e9\u30d5\u3067\u3059\u3002<\/p>\n\n\n \u3064\u307e\u308a\u3001\u6307\u6570\u65b9\u7a0b\u5f0f\u306e\u89e3\u3082\u305f\u30601\u3064\u306b\u5b9a\u307e\u308b<\/span>\u3053\u3068\u306b\u306a\u308a\u307e\u3059\u306d\u3002<\/p>\n\n\n \u6307\u6570\u95a2\u6570\u306b\u3064\u3044\u3066\u3082\u3057\u3063\u304b\u308a\u7406\u89e3\u3057\u3066\u304a\u3053\u3046<\/p>\n<\/span><\/span><\/span><\/div><\/div><\/div><\/div>\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 \\[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 \u6307\u6570\u306b\u6587\u5b57\u304c\u3042\u308b\u3068\u4f55\u3092\u3059\u308c\u3070\u3044\u3044\u304b\u5206\u304b\u3089\u306a\u304f\u306a\u308a\u307e\u3059<\/p>\n<\/span><\/span><\/span><\/div><\/div><\/div><\/div>\n\n \u3053\u3053\u304b\u3089\u6307\u6570\u65b9\u7a0b\u5f0f\u306e\u89e3\u304d\u65b9\u3092\u89e3\u8aac\u3059\u308b\u3088\uff01<\/p>\n<\/span><\/span><\/span><\/div><\/div><\/div><\/div>\n\n\n \u6307\u6570\u65b9\u7a0b\u5f0f\u306e\u554f\u984c\u306f\u5927\u304d\u304f5\u3064\u306e\u30d1\u30bf\u30fc\u30f3\u3057\u304b\u3042\u308a\u307e\u305b\u3093\u3002<\/span><\/p>\n\n\n\n \u554f\u984c\u306b\u30d1\u30bf\u30fc\u30f3\u304c\u3042\u308b\u3068\u3044\u3046\u3053\u3068\u306f\u3001\u89e3\u304d\u65b9\u3092\u899a\u3048\u308c\u3070\u89e3\u3051\u308b\u554f\u984c\u304c\u30b0\u30c3\u3068\u5e83\u304c\u308a\u307e\u3059\u3002<\/span><\/p>\n\n\n\n \u3053\u306e\u554f\u984c\u306e\u3068\u304d\u306f\u3069\u3046\u3059\u308b\u306e\u304b\u3001\u305d\u3046\u3044\u3063\u305f\u30a2\u30d7\u30ed\u30fc\u30c1\u306e\u4ed5\u65b9\u3092\u7406\u89e3\u3057\u3066\u3044\u304d\u307e\u3057\u3087\u3046\u3002<\/p>\n\n\n \u305d\u308c\u3067\u306f\u30011\u3064\u305a\u3064\u89e3\u8aac\u3057\u3066\u3044\u304d\u307e\u3059<\/p>\n<\/span><\/span><\/span><\/div><\/div><\/div><\/div>\n\n\n \u307e\u305a\u306f1\u756a\u30b7\u30f3\u30d7\u30eb\u306a\u554f\u984c\u304b\u3089\u7d39\u4ecb\u3057\u307e\u3059\u3002<\/p>\n\n\n\n \u6b21\u306e\u65b9\u7a0b\u5f0f\u3092\u89e3\u3044\u3066\u307f\u3088\u3046\u3002<\/p>\n\n\n\n (1) \\(2^{x}=8\\)<\/p>\n\n\n\n (2) \\(9^{x}=27\\)<\/p>\n<\/div><\/div>\n\n\n\n \u3053\u306e\u554f\u984c\u306f\u4e21\u8fba\u306e\u5e95\u3092\u63c3\u3048\u308b\u3053\u3068\u3067\u3001\u6307\u6570\u3092\u6bd4\u8f03\u3057\u3066\u89e3\u3092\u6c42\u3081\u307e\u3059\u3002<\/p>\n\n\n\n \u4e21\u8fba\u3092\u5e95\u304c\u540c\u3058\u7d2f\u4e57\u3067\u8868\u3059\u3053\u3068\u3092\u76ee\u6a19\u306b\u8003\u3048\u307e\u3057\u3087\u3046\u3002<\/span><\/p>\n\n\n\n \\begin{eqnarray} (2)\u306f\u4e21\u8fba\u3092\u5e953\u306e\u7d2f\u4e57\u306b\u76f4\u3059\u3068\u89e3\u3092\u6c42\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n \\begin{eqnarray} \u5f0f\u5909\u5f62\u306e\u9014\u4e2d\u306b\u6307\u6570\u6cd5\u5247\u3092\u4f7f\u3063\u305f\u8a08\u7b97\u304c\u3042\u308a\u307e\u3057\u305f\u306d\u3002<\/p>\n\n\n\n \u300c\u4f55\u304c\u8d77\u3053\u3063\u305f\uff01\uff1f\u300d<\/span><\/p>\n\n\n\n \u305d\u3046\u601d\u3063\u305f\u4eba\u3082\u3044\u308b\u304b\u3082\u3057\u308c\u307e\u305b\u3093\u304c\u3001\u6307\u6570\u6cd5\u5247\u306f\u5f53\u305f\u308a\u524d\u306e\u3088\u3046\u306b\u4f7f\u308f\u308c\u307e\u3059\u3002<\/p>\n\n\n\n \\[(a^{m})^{n}=a^{mn}\\]<\/p>\n<\/div><\/div>\n\n\n\n \u6307\u6570\u306e\u8a08\u7b97\u304c\u4e0d\u5b89\u306a\u3072\u3068\u306f\u3001\u6307\u6570\u6cd5\u5247\u306e\u91cd\u8981\u516c\u5f0f<\/span>\u3092\u78ba\u8a8d\u3057\u307e\u3057\u3087\u3046\u3002 \u30eb\u30fc\u30c8\u3084\u5206\u6570\u306e\u6307\u6570\u8a08\u7b97\u304c\u82e6\u624b\u306a\u3072\u3068\u3082\u591a\u3044\u3067\u3059\u3088\u306d\u3002<\/p>\n\n\n\n \u6b21\u306e\u65b9\u7a0b\u5f0f\u3092\u89e3\u3044\u3066\u307f\u3088\u3046\u3002<\/p>\n\n\n\n (1) \\(\\displaystyle 8^{x}=\\frac{1}{16}\\)<\/p>\n\n\n\n (2) \\(2^{1-x}=\\sqrt[3]{2}\\)<\/p>\n<\/div><\/div>\n\n\n\n (1)\u306f\u4e21\u8fba\u3092\u5e952\u306e\u7d2f\u4e57\u306b\u76f4\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n\n\n\n \\begin{eqnarray} (2)\u306f\u30eb\u30fc\u30c8\u304c\u3042\u308a\u307e\u3059\u306d\u3002 \\begin{eqnarray} \u30eb\u30fc\u30c8\u3084\u5206\u6570\u306b\u95a2\u4fc2\u3059\u308b\u6307\u6570\u6cd5\u5247\u3082\u78ba\u8a8d\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n\n\n\n \\(a\u22600\\)\u3067\\(n\\)\u304c\u6574\u6570\u306e\u3068\u304d\u3001<\/p>\n\n\n\n \\[\\displaystyle a^{-n}=\\frac{1}{a^{n}},\u3000a^{\\frac{1}{n}}=\\sqrt[n]{a}\\]<\/p>\n<\/div><\/div>\n\n\n \u30eb\u30fc\u30c8\u304c\u82e6\u624b\u3060\u3063\u305f\u3051\u3069\u7406\u89e3\u3067\u304d\u307e\u3057\u305f\uff01<\/p>\n<\/span><\/span><\/span><\/div><\/div><\/div><\/div>\n\n\n \u6307\u6570\u65b9\u7a0b\u5f0f\u306b\u306f\u3053\u3093\u306a\u9577\u3044\u554f\u984c\u3082\u3042\u308a\u307e\u3059\u3002<\/p>\n\n\n\n \u6b21\u306e\u65b9\u7a0b\u5f0f\u3092\u89e3\u3044\u3066\u307f\u3088\u3046\u3002<\/p>\n\n\n\n \\[2^{2x}-6 \\cdot 2^{x} +8=0\\]<\/p>\n<\/div><\/div>\n\n\n\n \u3053\u306e\u6307\u6570\u65b9\u7a0b\u5f0f\u306f\\(2^{x}\\)\u3092\\(t\\)\u306b\u7f6e\u304d\u63db\u3048\u308b\u3068\u89e3\u304d\u3084\u3059\u304f\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n \\begin{eqnarray} \u3053\u308c\u306f\u89e3\u304d\u65b9\u3092\u77e5\u3089\u306a\u3044\u3068\u82e6\u6226\u3059\u308b\u554f\u984c\u3067\u3059\u306d\u3002<\/p>\n\n\n \u6587\u5b57\u3067\u7f6e\u304d\u63db\u3048\u308b\u89e3\u304d\u65b9\u3082\u899a\u3048\u3066\u304a\u304d\u307e\u3059\uff01<\/p>\n<\/span><\/span><\/span><\/div><\/div><\/div><\/div>\n\n\n \u4e21\u8fba\u3092\u540c\u3058\u5e95\u3067\u306f\u8868\u305b\u306a\u3044\u554f\u984c\u3082\u3042\u308a\u307e\u3059\u3002<\/p>\n\n\n\n \u6b21\u306e\u65b9\u7a0b\u5f0f\u3092\u89e3\u3044\u3066\u307f\u3088\u3046\u3002<\/p>\n\n\n\n (1) \\(2^{x}=5\\)<\/p>\n\n\n\n (2) \\(3^{x}=12\\)<\/p>\n<\/div><\/div>\n\n\n\n \u540c\u3058\u5e95\u3067\u8868\u305b\u306a\u3044\u3068\u304d\u306f\u3001\u4e21\u8fba\u306e\u5bfe\u6570\u3092\u3068\u308a\u307e\u3057\u3087\u3046\u3002<\/p>\n\n\n\n \u3053\u306e\u554f\u984c\u306e\u5834\u5408\u306f\u3001\\(log_{2}\\)\u306b\u3059\u308b\u3068\u8a08\u7b97\u3057\u3084\u3059\u3044\u3067\u3059\u3002<\/p>\n\n\n\n \\begin{eqnarray} (2)\u306e\u554f\u984c\u3082\u898b\u3066\u307f\u307e\u3057\u3087\u3046\u3002<\/p>\n\n\n\n \\begin{eqnarray} \u5bfe\u6570\u3092\u3068\u308b\u5f0f\u5909\u5f62\u306f\u5225\u5358\u5143\u3067\u3082\u4f7f\u3046\u304b\u3089\u899a\u3048\u3066\u304a\u3053\u3046\uff01<\/p>\n<\/span><\/span><\/span><\/div><\/div><\/div><\/div>\n\n\n \u6700\u5f8c\u306e\u30d1\u30bf\u30fc\u30f3\u306f\u9023\u7acb\u65b9\u7a0b\u5f0f\u3092\u3064\u304b\u3063\u3066\u8003\u3048\u307e\u3059\u3002<\/p>\n\n\n\n \u6b21\u306e\u65b9\u7a0b\u5f0f\u3092\u89e3\u3044\u3066\u307f\u3088\u3046\u3002<\/p>\n\n\n\n \\begin{eqnarray} \u3053\u308c\u306f\\(3^{x}=X,5^{y}=Y\\)\u306b\u7f6e\u304d\u63db\u3048\u308b\u3053\u3068\u3067\u3001\u9023\u7acb\u65b9\u7a0b\u5f0f\u3068\u3057\u3066\u8003\u3048\u307e\u3059\u3002<\/p>\n\n\n\n \\begin{eqnarray} \u3053\u308c\u3092\u89e3\u304f\u3053\u3068\u306b\u3088\u3063\u3066\u3001<\/p>\n\n\n\n \\[X=27,Y=25\\]<\/p>\n\n\n\n \u3057\u305f\u304c\u3063\u3066\u3001<\/p>\n\n\n\n \\[3^{x}=27,5^{y}=25\\]<\/p>\n\n\n\n \\[\u2234 x=3,y=2\\]<\/p>\n\n\n \u7f6e\u304d\u63db\u3048\u30d1\u30bf\u30fc\u30f3\u306e\u5fdc\u7528\u3067\u3082\u3042\u308b\u3093\u3067\u3059\u306d\uff01<\/p>\n<\/span><\/span><\/span><\/div><\/div><\/div><\/div>\n\n\n 5\u3064\u306e\u6307\u6570\u65b9\u7a0b\u5f0f\u306e\u89e3\u304d\u65b9\u3092\u4f7f\u3063\u3066\u7df4\u7fd2\u554f\u984c\u306b\u30c1\u30e3\u30ec\u30f3\u30b8\u3057\u3066\u307f\u307e\u3057\u3087\u3046\u3002<\/p>\n\n\n\n \u6b21\u306e\u65b9\u7a0b\u5f0f\u3092\u89e3\u3044\u3066\u307f\u3088\u3046\u3002<\/p>\n\n\n\n (1) \\(\\displaystyle \\left(\\frac{1}{2} \\right)^{x-1}=(\\sqrt{2})^{x}\\)<\/p>\n\n\n\n (2) \\(9^{x}-10 \\cdot 3^{x}+9=0\\)<\/p>\n\n\n\n (3) \\(3^{x}=7^{x+1}\\)<\/p>\n<\/div><\/div>\n\n\n \u3069\u3046\u3084\u3063\u3066\u89e3\u304f\u306e\u304b\u8003\u3048\u308b\u3060\u3051\u3067\u3082\u7df4\u7fd2\u306b\u306a\u308b\u3088<\/p>\n<\/span><\/span><\/span><\/div><\/div><\/div><\/div>\n\n\n \u6b21\u306e\u65b9\u7a0b\u5f0f\u3092\u89e3\u3044\u3066\u307f\u3088\u3046\u3002<\/p>\n\n\n\n (1)\\(\\displaystyle \\left(\\frac{1}{2} \\right)^{x-1}=(\\sqrt{2})^{x}\\)<\/p>\n<\/div><\/div>\n\n\n\n \u3053\u306e\u554f\u984c\u306f\u5206\u6570\u3068\u30eb\u30fc\u30c8\u304c\u3042\u308b\u306e\u3067\u96e3\u3057\u305d\u3046\u306b\u898b\u3048\u307e\u3059\u304c\u3001\u5e95\u3092\u305d\u308d\u3048\u3066\u89e3\u3044\u3066\u3044\u304d\u307e\u3059\u3002<\/p>\n\n\n\n \\begin{eqnarray} \u3053\u308c\u3067\u65b9\u7a0b\u5f0f\u3092\u89e3\u304f\u3053\u3068\u304c\u3067\u304d\u307e\u3057\u305f\u3002<\/p>\n\n\n\n \u89e3\u304d\u65b9\u3092\u5fd8\u308c\u3066\u3057\u307e\u3063\u305f\u65b9\u306f\u3001\u5e95\u3092\u305d\u308d\u3048\u308b\u554f\u984c\u306e\u89e3\u304d\u65b9<\/a>\u306b\u623b\u3063\u3066\u5fa9\u7fd2\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n\n\n \u6307\u6570\u65b9\u7a0b\u5f0f\u306e\u57fa\u672c\u3068\u306a\u308b\u8003\u3048\u65b9\u3060\u306d<\/p>\n<\/span><\/span><\/span><\/div><\/div><\/div><\/div>\n\n\n \u6b21\u306e\u65b9\u7a0b\u5f0f\u3092\u89e3\u3044\u3066\u307f\u3088\u3046\u3002<\/p>\n\n\n\n (2) \\(9^{x}-10 \\cdot 3^{x}+9=0\\)<\/p>\n<\/div><\/div>\n\n\n\n \u3053\u306e\u554f\u984c\u306f\u3044\u3063\u305f\u3093\u9055\u3046\u6587\u5b57\u306b\u7f6e\u304d\u63db\u3048\u308b\u554f\u984c\u3067\u3057\u305f\u306d\u3002<\/p>\n\n\n\n \u4eca\u56de\u306f\\(3^{x}\\)\u3092\\(t\\)\u306b\u7f6e\u304d\u63db\u3048\u3066\u8003\u3048\u307e\u3057\u3087\u3046\u3002<\/p>\n\n\n\n \\begin{eqnarray} \\(t\\)\u304c\u6c42\u307e\u3063\u305f\u3068\u3053\u308d\u3067\u3001\\(t\\)\u3092\\(3^{x}\\)\u306b\u623b\u3057\u307e\u3059\u3002<\/p>\n\n\n\n \\begin{eqnarray} \u8a08\u7b97\u3092\u3057\u3084\u3059\u304f\u3059\u308b\u305f\u3081\u306b\u3001\u4f55\u3092\u6587\u5b57\u306b\u7f6e\u304d\u63db\u3048\u308b\u304b\u304c\u30dd\u30a4\u30f3\u30c8\uff01<\/p>\n\n\n\n
\u300c\u30eb\u30fc\u30c8\u3084\u5206\u6570\u304c\u3042\u3063\u3066\u56f0\u3063\u3066\u3044\u308b\u300d<\/span>
\u4eca\u56de\u306f\u6307\u6570\u65b9\u7a0b\u5f0f\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>
\u30b7\u30fc\u30bf<\/span><\/div>
\u305c\u3072\u6700\u5f8c\u307e\u3067\u3054\u89a7\u304f\u3060\u3055\u3044<\/p>\n<\/span><\/span><\/span><\/div><\/div><\/div><\/div>\n\n\n\u6307\u6570\u95a2\u6570\u3068\u306f\uff1f<\/h2>\n\n\n\n
<\/figure>\n<\/div>\n\n\n
\u6307\u6570\u95a2\u6570\u306e\u30b0\u30e9\u30d5\u304b\u3089\u5206\u304b\u308b\u3088\u3046\u306b\u3001\\(a^{x}=y\\)\u3092\u6e80\u305f\u3059\\(x\\)\u306f\u305f\u30601\u3064\u306b\u5b9a\u307e\u308a\u307e\u3059\u3002<\/p>\n\n\n\n
\u30b7\u30fc\u30bf<\/span><\/div>\u6307\u6570\u65b9\u7a0b\u5f0f<\/h2>\n\n\n\n
\u9ad8\u6821\u751f<\/span><\/div>
\u30b7\u30fc\u30bf<\/span><\/div>\u6307\u6570\u65b9\u7a0b\u5f0f\u306e\u89e3\u304d\u65b9<\/h2>\n\n\n\n
\n
\u30b7\u30fc\u30bf<\/span><\/div>\u5e95\u3092\u305d\u308d\u3048\u308b\u554f\u984c<\/h3>\n\n\n\n
2^{x}&=&8\\\\
2^{x}&=&2^{3}\\\\
x&=&3
\\end{eqnarray}<\/p>\n\n\n\n
9^{x}&=&27\\\\
(3^{2})^{x}&=&3^{3}\\\\
3^{2x}&=&3^{3}\\\\
2x&=&3\\\\
\\displaystyle x&=&\\frac{3}{2}
\\end{eqnarray}<\/p>\n\n\n\n
\u21d2\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<\/p>\n\n\n\n\u30eb\u30fc\u30c8\u3084\u5206\u6570\u304c\u3042\u308b\u554f\u984c<\/h3>\n\n\n\n
\\displaystyle 8^{x}&=&\\frac{1}{16}\\\\
\\displaystyle 2^{3x}&=&\\frac{1}{2^{4}}\\\\
2^{3x}&=&2^{-4}\\\\
3x&=&-4\\\\
\\displaystyle x&=&-\\frac{4}{3}
\\end{eqnarray}<\/p>\n\n\n\n
\u30eb\u30fc\u30c8\u306f\u6307\u6570\u304c\u5206\u6570\u306e\u7d2f\u4e57\u306b\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n
2^{1-x}&=&\\sqrt[3]{2}\\\\
\\displaystyle 2^{1-x}&=&2^{\\frac{1}{3}}\\\\
\\displaystyle 1-x&=&\\frac{1}{3}\\\\
\\displaystyle x&=&\\frac{2}{3}\\\\
\\end{eqnarray}<\/p>\n\n\n\n
\u9ad8\u6821\u751f<\/span><\/div>\u7f6e\u304d\u63db\u3048\u308b\u554f\u984c<\/h3>\n\n\n\n
t^{2}-6t+8&=&0\\\\
(t-2)(t-4)&=&0\\\\
t&=&2,4
\\end{eqnarray}
\\(t\\)\u3092\\(2^{x}\\)\u306b\u623b\u3057\u3066\u3001
\\begin{eqnarray}
2^{x}&=&2,4\\\\
x&=&1,2
\\end{eqnarray}<\/p>\n\n\n\n
\u9ad8\u6821\u751f<\/span><\/div>\u5bfe\u6570\u3092\u3068\u308b\u554f\u984c<\/h3>\n\n\n\n
2^{x}&=&5\\\\
log_{2}2^{x}&=&log_{2}5\\\\
x log_{2}2&=&log_{2}5\\\\
x&=&log_{2}5
\\end{eqnarray}<\/p>\n\n\n\n
3^{x}&=&12\\\\
log_{3}3^{x}&=&log_{3}12\\\\
x log_{3}3&=&log_{3}(3 \\cdot 4)\\\\
x&=&log_{3}3+log_{3}2^{2}\\\\
x&=&1+2 log_{3}2
\\end{eqnarray}<\/p>\n\n\n
\u30b7\u30fc\u30bf<\/span><\/div>\u9023\u7acb\u65b9\u7a0b\u5f0f\u306e\u554f\u984c<\/h3>\n\n\n\n
2 \\cdot 3^{x}+5^{y}&=&79 \\\\
3^{x}+2 \\cdot 5^{y}&=&77
\\end{eqnarray}<\/p>\n<\/div><\/div>\n\n\n\n
2 \\cdot X+Y&=&79 \\\\
X+2 \\cdot Y&=&77
\\end{eqnarray}<\/p>\n\n\n\n
\u9ad8\u6821\u751f<\/span><\/div>\u6307\u6570\u65b9\u7a0b\u5f0f\u300a\u7df4\u7fd2\u554f\u984c\u300b<\/h2>\n\n\n\n
\u30b7\u30fc\u30bf<\/span><\/div>\u7df4\u7fd2\u554f\u984c1\u306e\u89e3\u8aac<\/h3>\n\n\n\n
\\displaystyle \\left(\\frac{1}{2} \\right)^{x-1}&=&(\\sqrt{2})^{x}\\\\
\\displaystyle (2^{-1})^{x-1}&=&(2^{\\frac{1}{2}})^{x}\\\\
\\displaystyle 2^{1-x}&=&2^{\\frac{1}{2} x}\\\\
\\displaystyle 1-x&=&\\frac{1}{2}x\\\\
\\displaystyle x&=&\\frac{2}{3}
\\end{eqnarray}<\/p>\n\n\n\n
\u30b7\u30fc\u30bf<\/span><\/div>\u7df4\u7fd2\u554f\u984c2\u306e\u89e3\u8aac<\/h3>\n\n\n\n
9^{x}-10 \\cdot 3^{x}+9&=&0\\\\
3^{2x}-10 \\cdot 3^{x}+9&=&0\\\\
t^{2}-10t+9&=&0\\\\
(t-1)(t-9)&=&0\\\\
t&=&1,9\\\\
\\end{eqnarray}<\/p>\n\n\n\n
3^{x}&=&1,9\\\\
3^{x}&=&3^{0},3^{2}\\\\
x&=&0,2
\\end{eqnarray}<\/p>\n\n\n\n