{"id":11543,"date":"2022-12-10T00:00:08","date_gmt":"2022-12-09T15:00:08","guid":{"rendered":"https:\/\/hatsudy.com\/jp\/?p=11543"},"modified":"2022-12-12T04:54:58","modified_gmt":"2022-12-11T19:54:58","slug":"logarithm-3","status":"publish","type":"post","link":"https:\/\/hatsudy.com\/jp\/logarithm-3.html","title":{"rendered":"\u5e38\u7528\u5bfe\u6570\uff1a\u6841\u6570\u3068\u5c0f\u6570\u306e\u4f4d\u306e\u8a08\u7b97\u3001\u6700\u9ad8\u4f4d\u306e\u6570"},"content":{"rendered":"\n<p>\u5bfe\u6570\u306e\u4e2d\u3067\u3082\u3001\u7279\u6b8a\u306a\u5bfe\u6570\u306b\u5e38\u7528\u5bfe\u6570\u304c\u3042\u308a\u307e\u3059\u3002\u5e95\u304c10\u306e\u5834\u5408\u3001\u5e38\u7528\u5bfe\u6570\u3068\u547c\u3070\u308c\u307e\u3059\u3002\u5e38\u7528\u5bfe\u6570\u306e\u8a08\u7b97\u65b9\u6cd5\u306f\u4e00\u822c\u7684\u306a\u5bfe\u6570\u3068\u540c\u69d8\u3067\u3059\u3002<\/p>\n<p>\u6570\u5b57\u306e\u6841\u6570\u306e\u8a08\u7b97\u3092\u3057\u305f\u308a\u3001\u5c0f\u6570\u70b9\u306e\u4f4d\u3092\u8a08\u7b97\u3057\u305f\u308a\u3059\u308b\u3068\u304d\u3001\u5e38\u7528\u5bfe\u6570\u306f\u4fbf\u5229\u3067\u3059\u3002\u5b9f\u969b\u306e\u8a08\u7b97\u3092\u3057\u306a\u304f\u3066\u3082\u3001\u6841\u6570\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u306e\u3067\u3059\u3002<\/p>\n<p>\u5e38\u7528\u5bfe\u6570\u306f\u65e5\u5e38\u751f\u6d3b\u306e\u591a\u304f\u306e\u5834\u9762\u3067\u5229\u7528\u3055\u308c\u3066\u3044\u307e\u3059\u3002\u307e\u305f\u7269\u7406\u3084\u5316\u5b66\u306a\u3069\u306e\u79d1\u5b66\u5206\u91ce\u3067\u306f\u3001\u5e38\u7528\u5bfe\u6570\u3092\u7528\u3044\u3066\u306e\u8a08\u7b97\u304c\u3072\u3093\u3071\u3093\u306b\u5229\u7528\u3055\u308c\u307e\u3059\u3002\u305d\u306e\u305f\u3081\u3001\u5e38\u7528\u5bfe\u6570\u306e\u6982\u5ff5\u3092\u5b66\u3070\u306a\u3051\u308c\u3070\u3044\u3051\u307e\u305b\u3093\u3002<\/p>\n<p>\u305d\u308c\u3067\u306f\u3001\u3069\u306e\u3088\u3046\u306b\u5e38\u7528\u5bfe\u6570\u3092\u7528\u3044\u3066\u6841\u6570\u306e\u8a08\u7b97\u3092\u3059\u308c\u3070\u3044\u3044\u306e\u3067\u3057\u3087\u3046\u304b\u3002\u5e38\u7528\u5bfe\u6570\u3092\u7528\u3044\u3066\u8a08\u7b97\u3059\u308b\u65b9\u6cd5\u3092\u89e3\u8aac\u3057\u3066\u3044\u304d\u307e\u3059\u3002<\/p>\n<h2>\u5e38\u7528\u5bfe\u6570\u306e\u5b9a\u7fa9\u3068\u610f\u5473<\/h2>\n<p>\u307e\u305a\u3001\u5e38\u7528\u5bfe\u6570\u3068\u306f\u4f55\u304b\u3092\u7406\u89e3\u3057\u307e\u3057\u3087\u3046\u3002\u5148\u307b\u3069\u8aac\u660e\u3057\u305f\u901a\u308a\u3001\u5e95\u309210\u3068\u3059\u308b\u5bfe\u6570\u304c\u5e38\u7528\u5bfe\u6570\u3067\u3059\u3002\\(N\\)\u3092\u6b63\u306e\u6570\u3068\u3059\u308b\u3068\u3001\u5e38\u7528\u5bfe\u6570\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8868\u3055\u308c\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(log_{10}N\\)<\/li>\n<\/ul>\n<p>\u5e38\u7528\u5bfe\u6570\u3092\u5229\u7528\u3057\u3066\u8a08\u7b97\u3059\u308b\u5834\u5408\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306a\u6570\u5b57\u3092\u4e0e\u3048\u3089\u308c\u3066\u3044\u308b\u3053\u3068\u304c\u591a\u3044\u3067\u3059\u3002<\/p>\n<ul>\n<li>\\(log_{10}2\u22520.3010\\)<\/li>\n<li>\\(log_{10}3\u22520.4771\\)<\/li>\n<li>\\(log_{10}7\u22520.8451\\)<\/li>\n<\/ul>\n<p>\u3053\u308c\u3089\u306e\u5024\u3092\u899a\u3048\u308b\u5fc5\u8981\u306f\u3042\u308a\u307e\u305b\u3093\u3002\u91cd\u8981\u306a\u306e\u306f\u3001\u3053\u308c\u3089\u306e\u6570\u5b57\u3092\u7528\u3044\u3066\u8a08\u7b97\u3067\u304d\u308b\u3053\u3068\u306b\u3042\u308a\u307e\u3059\u3002<\/p>\n<h3>\u6841\u6570\u306e\u8a08\u7b97\u3067\u5e38\u7528\u5bfe\u6570\u304c\u5229\u7528\u3055\u308c\u308b<\/h3>\n<p>\u6841\u6570\u306e\u8a08\u7b97\u3092\u3059\u308b\u3068\u304d\u3001\u5e38\u7528\u5bfe\u6570\u304c\u4fbf\u5229\u3067\u3059\u3002\u5e38\u7528\u5bfe\u6570\u3092\u5229\u7528\u3059\u308c\u3070\u3001\u7b54\u3048\u304c\u4f55\u30b1\u30bf\u306b\u306a\u308b\u306e\u304b\u5bb9\u6613\u306b\u308f\u304b\u308b\u304b\u3089\u3067\u3059\u3002\u6841\u6570\u3068\u5e38\u7528\u5bfe\u6570\u306e\u95a2\u4fc2\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<ul>\n<li>1\uff081\u30b1\u30bf\uff09\uff1a\\(log_{10}10^0=0\\)<\/li>\n<li>10\uff082\u30b1\u30bf\uff09\uff1a\\(log_{10}10^1=1\\)<\/li>\n<li>100\uff083\u30b1\u30bf\uff09\uff1a\\(log_{10}10^2=2\\)<\/li>\n<li>1000\uff084\u30b1\u30bf\uff09\uff1a\\(log_{10}10^3=3\\)<\/li>\n<li>10000\uff085\u30b1\u30bf\uff09\uff1a\\(log_{10}10^4=4\\)<\/li>\n<\/ul>\n<p>\u3053\u306e\u3088\u3046\u306b\u78ba\u8a8d\u3059\u308b\u3068\u3001<span style=\"color: #0000ff;\">\u6841\u6570\u306b\u5bfe\u3057\u30661\u3092\u5f15\u304f\u3053\u3068\u306b\u3088\u308a\u3001\u5e38\u7528\u5bfe\u6570\u306e\u6570\u5b57\u3068\u4e00\u81f4\u3059\u308b\u3068\u308f\u304b\u308a\u307e\u3059\u3002<\/span>\u307e\u305f\u5e38\u7528\u5bfe\u6570\u306e\u7b54\u3048\u304c2.1\u30842.5\u3067\u3042\u3063\u3066\u3082\u3001\u6841\u6570\u306f\u4e8c\u30b1\u30bf\u3067\u3059\u30023\u30b1\u30bf\u306b\u306a\u308b\u305f\u3081\u306b\u306f\u3001\u5fc5\u305a10\u306e3\u4e57\u3067\u306a\u3051\u308c\u3070\u3044\u3051\u307e\u305b\u3093\u300210\u30922.1\u4e57\u3057\u305f\u308a\u30012.5\u4e57\u3057\u305f\u308a\u3059\u308b\u5834\u5408\u3001\u7b54\u3048\u306f3\u30b1\u30bf\u3067\u306f\u306a\u304f2\u30b1\u30bf\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<p>\u4f8b\u3048\u3070100\u30b1\u30bf\u306e\u6570\u5b57\u306e\u5834\u5408\u3001\u5e38\u7528\u5bfe\u6570\u3092\u5229\u7528\u3059\u308b\u3068\u3001\u6570\u5b57\u3068\u3057\u306699\u3092\u5f97\u3089\u308c\u307e\u3059\u3002\u305d\u308c\u3067\u306f\u3001\u4ee5\u4e0b\u306e\u554f\u984c\u306e\u7b54\u3048\u306f\u4f55\u3067\u3057\u3087\u3046\u304b\u3002<\/p>\n<ul>\n<li>\\(2^{100}\\)\u306f\u4f55\u30b1\u30bf\u306e\u6574\u6570\u3067\u3057\u3087\u3046\u304b\u3002\\(log_{10}2=0.3010\\)\u3092\u7528\u3044\u3066\u8a08\u7b97\u3057\u307e\u3057\u3087\u3046\u3002<\/li>\n<\/ul>\n<p>\u5e38\u7528\u5bfe\u6570\u3092\u7528\u3044\u3066\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8a08\u7b97\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\\(log_{10}2^{100}\\)<\/p>\n<p>\\(=100log_{10}2\\)<\/p>\n<p>\\(=100\u00d70.3010\\)<\/p>\n<p>\\(=30.10\\)<\/p>\n<p>\u5e38\u7528\u5bfe\u6570\u3092\u52a0\u3048\u308b\u3053\u3068\u306b\u3088\u3063\u3066\u300130.10\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3057\u305f\u3002\u3053\u308c\u306f\u3064\u307e\u308a\u3001\\(2^{100}\\)\u306f31\u30b1\u30bf\u306e\u6570\u5b57\u3067\u3042\u308b\u3053\u3068\u3092\u610f\u5473\u3057\u3066\u3044\u307e\u3059\u3002\\(2^{100}\\)\u306e\u8a08\u7b97\u3092\u3057\u306a\u304f\u3066\u3082\u3001\u5e38\u7528\u5bfe\u6570\u3092\u5229\u7528\u3059\u308c\u3070\u6841\u6570\u306e\u8a08\u7b97\u304c\u53ef\u80fd\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<h3>\u5c0f\u6570\u70b9\u306e\u4f4d\u3092\u8a08\u7b97\u3059\u308b<\/h3>\n<p>\u5927\u304d\u3044\u6570\u5b57\u306e\u6841\u6570\u3092\u8a08\u7b97\u3067\u304d\u308b\u306e\u3067\u3042\u308c\u3070\u3001\u5e38\u7528\u5bfe\u6570\u3092\u7528\u3044\u3066\u5c0f\u3055\u3044\u6570\u306e\u8a08\u7b97\u3082\u53ef\u80fd\u3067\u3059\u3002<span style=\"color: #0000ff;\">\u5c0f\u6570\u7b2c\u4f55\u4f4d\u3067\u521d\u3081\u30660\u3067\u306f\u306a\u3044\u6570\u5b57\u304c\u8868\u308c\u308b\u306e\u304b\u8a08\u7b97\u3057\u305f\u3044\u5834\u5408\u3001\u5e38\u7528\u5bfe\u6570\u304c\u4fbf\u5229\u3067\u3059\u3002<\/span><\/p>\n<p>\u305d\u3053\u3067\u3001\u5c0f\u6570\u3068\u5e38\u7528\u5bfe\u6570\u306e\u95a2\u4fc2\u3092\u5b66\u3073\u307e\u3057\u3087\u3046\u3002\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<ul>\n<li>0.1\uff1a\\(log_{10}10^{-1}=-1\\)<\/li>\n<li>0.01\uff1a\\(log_{10}10^{-2}=-2\\)<\/li>\n<li>0.001\uff1a\\(log_{10}10^{-3}=-3\\)<\/li>\n<li>0.0001\uff1a\\(log_{10}10^{-4}=-4\\)<\/li>\n<li>0.00001\uff1a\\(log_{10}10^{-5}=-5\\)<\/li>\n<\/ul>\n<p>\u3053\u306e\u3088\u3046\u306b\u78ba\u8a8d\u3059\u308b\u3068\u3001\u5c0f\u6570\u7b2c\\(k\\)\u4f4d\u3067\u521d\u3081\u30660\u3067\u306f\u306a\u3044\u6570\u5b57\u304c\u8868\u308c\u308b\u5834\u5408\u3001\u5e38\u7528\u5bfe\u6570\u306e\u6570\u5b57\u306f\\(-k\\)\u306b\u306a\u308b\u3068\u308f\u304b\u308a\u307e\u3059\u3002\u4f8b\u3048\u3070\u5e38\u7528\u5bfe\u6570\u3092\u5229\u7528\u3057\u3066\u5f97\u305f\u7b54\u3048\u304c-2.1\u306e\u5834\u5408\u3001\u5c0f\u6570\u7b2c2\u4f4d\u3067\u521d\u3081\u30660\u4ee5\u5916\u306e\u6570\u5b57\u304c\u8868\u308c\u307e\u3059\u3002<\/p>\n<p>\u305d\u308c\u3067\u306f\u3001\u4ee5\u4e0b\u306e\u554f\u984c\u306e\u7b54\u3048\u306f\u4f55\u3067\u3057\u3087\u3046\u304b\u3002<\/p>\n<ul>\n<li>\\(\\left(\\displaystyle\\frac{1}{2}\\right)^{100}\\)\u3092\u5c0f\u6570\u3067\u8868\u3059\u3068\u304d\u3001\u5c0f\u6570\u7b2c\u4f55\u4f4d\u306b\u521d\u3081\u30660\u3067\u306f\u306a\u3044\u6570\u5b57\u304c\u8868\u308c\u308b\u3067\u3057\u3087\u3046\u304b\u3002\\(log_{10}2=0.3010\\)\u3092\u7528\u3044\u3066\u8a08\u7b97\u3057\u307e\u3057\u3087\u3046\u3002<\/li>\n<\/ul>\n<p>\u5e38\u7528\u5bfe\u6570\u3092\u7528\u3044\u3066\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8a08\u7b97\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\\(log_{10}\\left(\\displaystyle\\frac{1}{2}\\right)^{100}\\)<\/p>\n<p>\\(=100log_{10}\\displaystyle\\frac{1}{2}\\)<\/p>\n<p>\\(=100(log_{10}1-log_{10}2)\\)<\/p>\n<p>\\(=100\u00d7-log_{10}2\\)<\/p>\n<p>\\(=100\u00d7-0.3010\\)<\/p>\n<p>\\(=-30.10\\)<\/p>\n<p>\u3053\u3046\u3057\u3066\u5e38\u7528\u5bfe\u6570\u3092\u7528\u3044\u3066\u8a08\u7b97\u3059\u308b\u3068\u3001\u7b54\u3048\u306f-30.10\u306b\u306a\u308b\u3068\u308f\u304b\u308a\u307e\u3057\u305f\u3002\u3064\u307e\u308a\u3001\u5c0f\u6570\u7b2c30\u4f4d\u3067\u521d\u3081\u30660\u3067\u306f\u306a\u3044\u6570\u5b57\u304c\u8868\u308c\u307e\u3059\u3002<\/p>\n<h2>\u5e38\u7528\u5bfe\u6570\u3068\u4e0d\u7b49\u5f0f\u306e\u8a08\u7b97<\/h2>\n<p>\u6b21\u306b\u3001\u5e38\u7528\u5bfe\u6570\u3068\u4e0d\u7b49\u5f0f\u3092\u7528\u3044\u3066\u8a08\u7b97\u3067\u304d\u308b\u3088\u3046\u306b\u306a\u308a\u307e\u3057\u3087\u3046\u3002\u524d\u8ff0\u306e\u901a\u308a\u3001\u5e38\u7528\u5bfe\u6570\u3092\u7528\u3044\u3066\u6841\u6570\u306e\u8a08\u7b97\u304c\u53ef\u80fd\u3067\u3059\u3002\u4f8b\u3048\u3070\\(k\\)\u30b1\u30bf\u306e\u6570\u5b57\u306b\u3064\u3044\u3066\u3001\u6574\u6570\\(N\\)\u3068\u306e\u95a2\u4fc2\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(k-1\u2266log_{10}N&lt;k\\)<\/li>\n<\/ul>\n<p>\u65e2\u306b\u8aac\u660e\u3057\u305f\u5185\u5bb9\u3067\u3042\u308b\u305f\u3081\u3001\u3053\u308c\u306b\u3064\u3044\u3066\u306f\u554f\u984c\u306a\u304f\u7406\u89e3\u3067\u304d\u308b\u3068\u601d\u3044\u307e\u3059\u3002\u3053\u306e\u6027\u8cea\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u306b\u3088\u308a\u3001\u6841\u6570\u306b\u95a2\u308f\u308b\u554f\u984c\u3092\u89e3\u304f\u306e\u3067\u3059\u3002\u4f8b\u984c\u3068\u3057\u3066\u3001\u4ee5\u4e0b\u306e\u554f\u984c\u3092\u89e3\u304d\u307e\u3057\u3087\u3046\u3002<\/p>\n<ul>\n<li>\\(3^n\\)\u304c10\u30b1\u30bf\u306e\u6570\u3068\u306a\u308b\u6700\u5c0f\u306e\u81ea\u7136\u6570\\(n\\)\u3092\u6c42\u3081\u307e\u3057\u3087\u3046\u3002\u306a\u304a\u3001\\(log_{10}3=0.4771\\)\u3067\u3059\u3002<\/li>\n<\/ul>\n<p>\u5e38\u7528\u5bfe\u6570\u3092\u5229\u7528\u3057\u3066\u8a08\u7b97\u3059\u308b\u3068\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<p>\\(log_{10}3^n\\)<\/p>\n<p>\\(=nlog_{10}3\\)<\/p>\n<p>\\(=0.4771n\\)<\/p>\n<p>10\u30b1\u30bf\u306e\u6570\u3068\u306a\u308b\u305f\u3081\u306b\u306f\u3001\u4ee5\u4e0b\u306e\u6761\u4ef6\u3092\u6e80\u305f\u3059\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(9\u22660.4771n&lt;10\\)<\/li>\n<\/ul>\n<p>\u305d\u3053\u3067\u3001\u3053\u306e\u6761\u4ef6\u3092\u6e80\u305f\u3059\u6700\u5c0f\u306e\u81ea\u7136\u6570\\(n\\)\u3092\u8a08\u7b97\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\\(9\u22660.4771n&lt;10\\)<\/p>\n<p>\\(\\displaystyle\\frac{9}{0.4771}\u2266n&lt;\\displaystyle\\frac{10}{0.4771}\\)<\/p>\n<p>\\(18.86&#8230;\u2266n&lt;20.95&#8230;\\)<\/p>\n<p>\u3053\u3046\u3057\u3066\u3001\u6700\u5c0f\u306e\u81ea\u7136\u6570\\(n\\)\u306f19\u3067\u3042\u308b\u3068\u308f\u304b\u308a\u307e\u3057\u305f\u3002\u53c2\u8003\u307e\u3067\u306b\u3001\u5f0f\u3092\u78ba\u8a8d\u3057\u3066\u308f\u304b\u308b\u901a\u308a\\(n=19\\)\u307e\u305f\u306f\\(n=20\\)\u306e\u3068\u304d\u3001\\(3^n\\)\u306f10\u30b1\u30bf\u306e\u6570\u306b\u306a\u308b\u3068\u308f\u304b\u308a\u307e\u3059\u3002<\/p>\n<h3>\u5e38\u7528\u5bfe\u6570\u306b\u3088\u3063\u3066\u6700\u9ad8\u4f4d\u306e\u6570\u3068\u4e00\u306e\u4f4d\u306e\u6570\u3092\u5f97\u308b<\/h3>\n<p>\u6b21\u306b\u3001\u6700\u9ad8\u4f4d\u306e\u6570\u3068\u4e00\u306e\u4f4d\u306e\u6570\u3092\u8a08\u7b97\u3067\u304d\u308b\u3088\u3046\u306b\u306a\u308a\u307e\u3057\u3087\u3046\u3002\u6700\u9ad8\u4f4d\u306e\u6570\u3068\u306f\u3001\u4e00\u756a\u5de6\u306b\u5b58\u5728\u3059\u308b\u6570\u5b57\u3092\u6307\u3057\u307e\u3059\u3002\u4f8b\u3048\u307084625\u3067\u3042\u308c\u3070\u30018\u304c\u6700\u9ad8\u4f4d\u306e\u6570\u3067\u3059\u3002<\/p>\n<p>\u305d\u308c\u3067\u306f\u3001\u3069\u306e\u3088\u3046\u306b\u8003\u3048\u3066\u6700\u9ad8\u4f4d\u306e\u6570\u3092\u8a08\u7b97\u3059\u308c\u3070\u3044\u3044\u306e\u3067\u3057\u3087\u3046\u304b\u3002\u5177\u4f53\u7684\u306a\u6570\u5b57\u3092\u5229\u7528\u3057\u3066\u8003\u3048\u3066\u3044\u304d\u307e\u3057\u3087\u3046\u3002\u4f8b\u3048\u3070300\u306f3\u30b1\u30bf\u306e\u6570\u5b57\u3067\u3059\u3002\u5e38\u7528\u5bfe\u6570\u3092\u5229\u7528\u3059\u308b\u3068\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8a08\u7b97\u3067\u304d\u307e\u3059\u3002<\/p>\n<p>\\(log_{10}300\\)<\/p>\n<p>\\(log_{10}100\u00d73\\)<\/p>\n<p>\\(=log_{10}10^2+log_{10}3\\)<\/p>\n<p>\\(=2+log_{10}3\\)<\/p>\n<p>2\u30b1\u30bf\u306e\u6570\u5b57\u3067\u3042\u308b\u305f\u3081\u3001\u5e38\u7528\u5bfe\u6570\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u306b\u3088\u3063\u30662\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u305d\u308c\u306b\u52a0\u3048\u3066\u3001\\(log_{10}3\\)\u3092\u52a0\u3048\u308b\u3068\\(log_{10}300\\)\u306b\u306a\u308a\u307e\u3059\u3002\u540c\u69d8\u306b\u8a08\u7b97\u3059\u308b\u3068\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(log_{10}100=2\\)<\/li>\n<li>\\(log_{10}200=2+log_{10}2\\)<\/li>\n<li>\\(log_{10}300=2+log_{10}3\\)<\/li>\n<li>\\(log_{10}400=2+log_{10}4\\)<\/li>\n<li>\\(log_{10}500=2+log_{10}5\\)<\/li>\n<li>\\(log_{10}600=2+log_{10}6\\)<\/li>\n<li>\\(log_{10}700=2+log_{10}7\\)<\/li>\n<li>\\(log_{10}800=2+log_{10}8\\)<\/li>\n<li>\\(log_{10}900=2+log_{10}9\\)<\/li>\n<\/ul>\n<p>\u3053\u306e\u3088\u3046\u306b\u78ba\u8a8d\u3059\u308b\u3068\u3001\u6841\u6570\u306b\u95a2\u308f\u3089\u306a\u3044\u90e8\u5206\uff08\\(+log_{10}k\\)\uff09\u3092\u78ba\u8a8d\u3059\u308c\u3070\u3001\u6700\u9ad8\u4f4d\u306e\u6570\u3092\u5224\u65ad\u3067\u304d\u308b\u3068\u308f\u304b\u308a\u307e\u3059\u3002\u4f8b\u3048\u3070\u5e38\u7528\u5bfe\u6570\u3092\u7528\u3044\u3066\u8a08\u7b97\u3057\u3001\u7b54\u3048\u304c\\(5+log_{10}3.2\\)\u306a\u306e\u3067\u3042\u308c\u3070\u3001\u6700\u9ad8\u4f4d\u306e\u6570\u304c3\u3067\u3042\u308b6\u30b1\u30bf\u306e\u6570\u3068\u308f\u304b\u308a\u307e\u3059\u3002<\/p>\n<p>\u8a08\u7b97\u65b9\u6cd5\u3092\u77e5\u3063\u3066\u3044\u306a\u3044\u3068\u6700\u9ad8\u4f4d\u306e\u6570\u3092\u5f97\u308b\u3053\u3068\u306f\u3067\u304d\u307e\u305b\u3093\u3002\u3044\u305a\u308c\u306b\u3057\u3066\u3082\u3001\u3053\u306e\u8003\u3048\u65b9\u306b\u3088\u3063\u3066\u6700\u9ad8\u4f4d\u306e\u6570\u3092\u6c42\u3081\u307e\u3057\u3087\u3046\u3002\u305d\u308c\u3067\u306f\u3001\u4ee5\u4e0b\u306e\u554f\u984c\u306e\u7b54\u3048\u306f\u4f55\u3067\u3057\u3087\u3046\u304b\u3002<\/p>\n<ul>\n<li>\\(9^{50}\\)\u306b\u3064\u3044\u3066\u3001\u6700\u9ad8\u4f4d\u306e\u6570\u3068\u4e00\u306e\u4f4d\u306e\u6570\u3092\u6c42\u3081\u307e\u3057\u3087\u3046\u3002\u306a\u304a\\(log_{10}2=0.3010\\)\u3001\\(log_{10}3=0.4771\\)\u3067\u3059\u3002<\/li>\n<\/ul>\n<p>\u307e\u305a\u3001\u5e38\u7528\u5bfe\u6570\u3092\u7528\u3044\u3066\u8a08\u7b97\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\\(log_{10}9^{50}\\)<\/p>\n<p>\\(=50log_{10}9\\)<\/p>\n<p>\\(=50log_{10}3^2\\)<\/p>\n<p>\\(=100log_{10}3\\)<\/p>\n<p>\\(=100\u00d70.4771\\)<\/p>\n<p>\\(=47.71\\)<\/p>\n<p>\u3053\u3046\u3057\u3066\u3001\\(9^{50}\\)\u306e\u6841\u6570\u306f48\u3068\u308f\u304b\u308a\u307e\u3059\u3002\u305d\u308c\u3067\u306f\u3001\u6700\u9ad8\u4f4d\u306e\u6570\u306f\u3044\u304f\u3089\u306b\u306a\u308b\u306e\u3067\u3057\u3087\u3046\u304b\u3002\u5148\u307b\u3069\u306e\u7d50\u679c\u3088\u308a\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8868\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(log_{10}9^{50}=47+0.71\\)<\/li>\n<\/ul>\n<p>\u305d\u308c\u3067\u306f\u5e38\u7528\u5bfe\u6570\u30670.71\u3068\u3044\u3046\u306e\u306f\u3001\\(log_{10}k\\)\u3067\u8868\u3059\u3068\u3001\u3069\u306e\u3088\u3046\u306b\u306a\u308b\u306e\u3067\u3057\u3087\u3046\u304b\u3002\u3053\u3053\u3067\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u3001\\(log_{10}5\\)\u3068\\(log_{10}6\\)\u3092\u8a08\u7b97\u3057\u3066\u307f\u307e\u3057\u3087\u3046\u3002<\/p>\n<p><strong>\u30fb\\(log_{10}5\\)\u306e\u8a08\u7b97<\/strong><\/p>\n<p>\\(log_{10}5\\)<\/p>\n<p>\\(=log_{10}\\displaystyle\\frac{10}{2}\\)<\/p>\n<p>\\(=log_{10}10-log_{10}2\\)<\/p>\n<p>\\(=1-0.3010\\)<\/p>\n<p>\\(=0.6990\\)<\/p>\n<p><strong>\u30fb\\(log_{10}6\\)\u306e\u8a08\u7b97<\/strong><\/p>\n<p>\\(log_{10}6\\)<\/p>\n<p>\\(=log_{10}2\u00d73\\)<\/p>\n<p>\\(=log_{10}2+log_{10}3\\)<\/p>\n<p>\\(=0.3010+0.4771\\)<\/p>\n<p>\\(=0.7781\\)<\/p>\n<p>\u3053\u306e\u7d50\u679c\u3088\u308a\u3001\u4ee5\u4e0b\u306e\u95a2\u4fc2\u304c\u3042\u308b\u3068\u308f\u304b\u308a\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(log_{10}5&lt;0.71&lt;log_{10}6\\)<\/li>\n<\/ul>\n<p>\u3064\u307e\u308a\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(log_{10}9^{50}=47+log_{10}5.\u2610\u2610\\)<\/li>\n<\/ul>\n<p>\\(\u2610\\)\u306b\u3069\u306e\u6570\u5b57\u304c\u5165\u308b\u306e\u304b\u306f\u308f\u304b\u308a\u307e\u305b\u3093\u3002\u305f\u3060\u5148\u307b\u3069\u89e3\u8aac\u3057\u305f\u901a\u308a\u3001\u5e38\u7528\u5bfe\u6570\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u3067\\(log_{10}5.\u2610\u2610\\)\u3092\u52a0\u3048\u308b\u3053\u3068\u306b\u306a\u308b\u305f\u3081\u3001\u6700\u9ad8\u4f4d\u306e\u6570\u306f5\u3068\u308f\u304b\u308a\u307e\u3059\u3002<\/p>\n<p><strong>\u30fb\u4e00\u306e\u4f4d\u306e\u6570\u3092\u6c42\u3081\u308b<\/strong><\/p>\n<p>\u306a\u304a\u3001\u4e00\u306e\u4f4d\u306e\u6570\u3092\u8a08\u7b97\u3059\u308b\u65b9\u6cd5\u306f\u7c21\u5358\u3067\u3059\u3002<span style=\"color: #0000ff;\">\u6570\u3092\u7d2f\u4e57\u3059\u308b\u5834\u5408\u3001\u6cd5\u5247\u6027\u304c\u3042\u308a\u307e\u3059\u3002<\/span>\u305d\u3053\u3067\u6cd5\u5247\u6027\u3092\u898b\u3064\u3051\u308b\u3053\u3068\u306b\u3088\u308a\u3001\u4e00\u306e\u4f4d\u306e\u6570\u3092\u8a08\u7b97\u3057\u307e\u3057\u3087\u3046\u3002\u4f8b\u3048\u30709\u306e\u7d2f\u4e57\u3067\u306f\u3001\u4e00\u306e\u4f4d\u306b\u7740\u76ee\u3059\u308b\u3068\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<ul>\n<li><span style=\"color: #ff0000;\">9<\/span>, 8<span style=\"color: #ff0000;\">1<\/span>, 72<span style=\"color: #ff0000;\">9<\/span>, 656<span style=\"color: #ff0000;\">1<\/span>, 5904<span style=\"color: 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