\n
\u6b21\u306e\u5f0f\u3092\u7c21\u5358\u306b\u3057\u3088\u3046\u3002<\/p>\n\n\n\n
\\[\\displaystyle \\frac{log_{2}5}{log_{3}5}\\]<\/p>\n<\/div><\/div>\n\n\n\n
\u3053\u308c\u306f\u5206\u6bcd\u30fb\u5206\u5b50\u306e\u5e95\u304c\u7570\u306a\u308b\u306e\u3067\u3001\u3053\u306e\u307e\u307e\u3067\u306f\u4f55\u3082\u3067\u304d\u305d\u3046\u306b\u3042\u308a\u307e\u305b\u3093\u3001<\/p>\n\n\n\n
\u305d\u3053\u3067\u5e95\u306e\u5909\u63db\u516c\u5f0f\u3092\u7528\u3044\u3066\u3001\u5206\u6bcd\u30fb\u5206\u5b50\u306e\u5e95\u3092\u540c\u3058\u306b\u3057\u307e\u3059\u3002<\/p>\n\n\n\n
\\begin{eqnarray}
\\displaystyle \\frac{log_{2}5}{log_{3}5}&=&log_{2}5 \\cdot \\frac{1}{log_{3}5}\\\\
\\displaystyle &=&log_{2}5 \\cdot \\frac{1}{\\frac{log_{2}5}{log_{2}3}}\\\\
\\displaystyle &=&log_{2}5 \\cdot \\frac{log_{2}3}{log_{2}5}\\\\
\\displaystyle &=&log_{2}3\\\\
\\end{eqnarray}<\/p>\n\n\n\n
\u5206\u6bcd\u30fb\u5206\u5b50\u304c\u5bfe\u6570\u306e\u3068\u304d\u306f\u3001\u5e95\u306e\u5909\u63db\u516c\u5f0f\u3092\u4f7f\u3063\u3066\u7c21\u5358\u306b\u3059\u308b\u3088\u3046\u306b\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n\n\n\n
\u5e95\u306e\u5909\u63db\u516c\u5f0f\u300a\u7df4\u7fd2\u554f\u984c\u300b<\/h2>\n\n\n\n
\u5e95\u306e\u5909\u63db\u516c\u5f0f\u3092\u4f7f\u3063\u3066\u7df4\u7fd2\u554f\u984c\u306b\u6311\u6226\u3057\u3066\u307f\u307e\u3057\u3087\u3046\u3002<\/p>\n\n\n\n
\u4ee5\u4e0b\u304c\u4eca\u56de\u306e\u7df4\u7fd2\u554f\u984c\u3067\u3059\u3002<\/p>\n\n\n\n
\u7df4\u7fd2\u554f\u984c<\/span><\/div>\n
\u6b21\u306e\u8a08\u7b97\u3092\u3057\u3066\u307f\u3088\u3046\u3002<\/p>\n\n\n\n
(1)\\(log_{2}3 \\cdot log_{3}4 \\cdot log_{4}5\\)<\/p>\n\n\n\n
(2)\\(log_{4}\\sqrt{8}\\)<\/p>\n\n\n\n
(3)\\(\\displaystyle \\frac{3}{log_{9}3}\\)<\/p>\n<\/div><\/div>\n\n\n
\u30b7\u30fc\u30bf<\/span><\/div>\n
\u982d\u306e\u4e2d\u3067\u65b9\u91dd\u3092\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\u7df4\u7fd2\u554f\u984c1\u306e\u89e3\u8aac<\/h3>\n\n\n\n
\u305d\u308c\u3067\u306f\u7df4\u7fd2\u554f\u984c\u306e\u89e3\u8aac\u3092\u3057\u3066\u3044\u304d\u307e\u3057\u3087\u3046\u3002<\/p>\n\n\n\n
\u7df4\u7fd2\u554f\u984c<\/span><\/div>\n
\u6b21\u306e\u8a08\u7b97\u3092\u3057\u3066\u307f\u3088\u3046\u3002<\/p>\n\n\n\n
(1)\\(log_{2}3 \\cdot log_{3}4 \\cdot log_{4}5\\)<\/p>\n<\/div><\/div>\n\n\n\n
\u3053\u308c\u306f\u5e95\u306e\u5909\u63db\u516c\u5f0f\u3092\u6d3b\u7528\u3059\u308b\u5178\u578b\u7684\u306a\u554f\u984c\u3067\u3059\u3002<\/p>\n\n\n\n
\\begin{eqnarray}
&&log_{2}3 \\cdot log_{3}4 \\cdot log_{4}5\\\\
&=&log_{2}3 \\cdot \\dfrac{log_{2}4}{log_{2}3} \\cdot \\dfrac{log_{2}5}{log_{2}4}\\\\
&=&log_{2}5
\\end{eqnarray}<\/p>\n\n\n\n
\u3053\u306e\u30bf\u30a4\u30d7\u306e\u554f\u984c\u306f\u3059\u3050\u306b\u624b\u304c\u52d5\u304b\u305b\u308b\u3088\u3046\u306b\u3057\u3066\u304a\u304d\u307e\u3057\u3087\u3046\u3002<\/p>\n\n\n
\u30b7\u30fc\u30bf<\/span><\/div>\n
\u5e95\u306e\u7570\u306a\u308b\u5bfe\u6570\u306e\u304b\u3051\u7b97\u304c\u76ee\u5370\u3067\u3059<\/p>\n<\/span><\/span><\/span><\/div><\/div><\/div><\/div>\n\n\n\u7df4\u7fd2\u554f\u984c2\u306e\u89e3\u8aac<\/h3>\n\n\n\n\u7df4\u7fd2\u554f\u984c<\/span><\/div>\n
\u6b21\u306e\u5f0f\u3092\u7c21\u5358\u306b\u3057\u3088\u3046\u3002<\/p>\n\n\n\n
(2)\\(log_{4}\\sqrt{8}\\)<\/p>\n<\/div><\/div>\n\n\n\n
\u771f\u6570\u306b\u30eb\u30fc\u30c8\u304c\u3042\u308b\u30bf\u30a4\u30d7\u306e\u554f\u984c\u3067\u3059\u3002<\/p>\n\n\n\n
\\begin{eqnarray}
log_{4}\\sqrt{8}&=&log_{4}8^{\\frac{1}{2}}\\\\
\\displaystyle &=&\\frac{1}{2}log_{4}8
\\end{eqnarray}<\/p>\n\n\n\n
\u30eb\u30fc\u30c8\u304c\u3044\u306a\u304f\u306a\u3063\u305f\u3068\u3053\u308d\u3067\u3001\u3055\u3089\u306b\u5f0f\u3092\u7c21\u5358\u306b\u3057\u3066\u3044\u304d\u307e\u3059<\/p>\n\n\n\n
\\begin{eqnarray}
&=&\\frac{1}{2}log_{4}8\\\\
\\displaystyle &=&\\frac{1}{2}log_{4}2^{3}\\\\
\\displaystyle &=&\\frac{3}{2}log_{4}2
\\end{eqnarray}<\/p>\n\n\n\n
\u3053\u308c\u3067\u5b8c\u6210\u306b\u898b\u3048\u307e\u3059\u304c\u3001\u5b9f\u306f\u3082\u3063\u3068\u7c21\u5358\u306b\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n
\\begin{eqnarray}
\\displaystyle &=&\\frac{3}{2}log_{4}2\\\\
\\displaystyle &=&\\frac{3}{2} \\cdot \\frac{log_{2}2}{log_{2}4}\\\\
\\displaystyle &=&\\frac{3}{2} \\cdot \\frac{1}{2}\\\\
\\displaystyle &=&\\frac{3}{4}
\\end{eqnarray}<\/p>\n\n\n
\u9ad8\u6821\u751f<\/span><\/div>\n
\u3053\u3093\u306a\u306b\u7c21\u5358\u306a\u5f62\u306b\u306a\u308a\u307e\u3057\u305f\uff01<\/p>\n