{"id":64874,"date":"2020-06-18T17:27:55","date_gmt":"2020-06-18T08:27:55","guid":{"rendered":"http:\/\/mechsys.tec.u-ryukyu.ac.jp\/~oshiro\/SiteList\/?p=64874"},"modified":"2020-07-04T17:33:02","modified_gmt":"2020-07-04T08:33:02","slug":"%e5%b8%b8%e7%94%a8%e5%af%be%e6%95%b0%e3%81%ae%e8%bf%91%e4%bc%bc%e5%80%a4%e3%81%ae%e7%ae%97%e5%87%ba","status":"publish","type":"post","link":"http:\/\/mechsys.tec.u-ryukyu.ac.jp\/~oshiro\/SiteList\/2020\/06\/18\/64874\/","title":{"rendered":"\u5e38\u7528\u5bfe\u6570\u306e\u8fd1\u4f3c\u5024\u306e\u7b97\u51fa"},"content":{"rendered":"<p>\u5bfe\u6570\u306f\u300c\u5e95$x$\u306e\u5024\u3092\u4f55\u4e57\u3057\u305f\u3089$z$\u306b\u306a\u308b\u304b\uff1f\u300d\u306e\u6307\u6570\u3092\u6c42\u3081\u308b\u3082\u306e\u3001\u6307\u5b9a\u3059\u308b\u3082\u306e\u3068\u6349\u3048\u308b\u3002<br \/>\n$z=x^y$\u3067\u306e$y$\u3092\u77e5\u308a\u305f\u3044\u5834\u5408\u306b$y=\\log_{x}z$\u3068\u66f8\u304f\u3002<\/p>\n<ul>\n<li><a href=\"http:\/\/mechsys.tec.u-ryukyu.ac.jp\/~oshiro\/SiteList\/2020\/07\/03\/67387\/\">\u5bfe\u6570\u95a2\u9023\u306e\u516c\u5f0f<\/a>\n<\/ul>\n<p>\n\u5e38\u7528\u5bfe\u6570\u306f\u3001\u5bfe\u6570\u306e\u5e95\u304c10\u306e\u3082\u306e\u3002<br \/>\n\uff08\u203b\u81ea\u7136\u5bfe\u6570\u306f\u5bfe\u6570\u306e\u5e95\u304ce\u306e\u3082\u306e\u3002${\\rm e}^x$\u306f\u5fae\u5206\u3057\u3066\u3082${\\rm e}^x$\u306e\u307e\u307e\u306a\u306e\u3067\u4fbf\u5229\uff09<\/p>\n<p>\n$\\log_{10} 1 = 0, (10^0=1)$<br \/>\n$\\log_{10} 2 \\fallingdotseq 0.3$<\/p>\n<div style=\"margin-left: 20px;\">\n  $\\log_{10} 2^{10}=\\log_{10} 1024\\fallingdotseq \\log_{10} 1000=\\log_{10}10^3=3\\log_{10}10=3\\cdot 1=3$<\/p>\n<p>\n  $\\Rightarrow 10\\log_{10}2\\fallingdotseq3 \\Rightarrow \\log_{10}2\\fallingdotseq \\displaystyle\\frac{3}{10}=0.3$\n<\/p><\/div>\n<p>$\\log_{10}3\\fallingdotseq 0.475, (10^{0.5}=\\sqrt{10}\\fallingdotseq \\sqrt{9}=3)$<\/p>\n<div style=\"margin-left: 20px;\">\n  $\\log_{10}3^4=\\log_{10}(9\\cdot 9)=\\log_{10}{81}\\fallingdotseq \\log_{10}80=\\log_{10}(2^3\\cdot 10) \\Rightarrow 3\\log_{10}2 + \\log_{10}10 \\fallingdotseq 3\\cdot 0.3 + 1 = 1.9$<br \/>\n  $\\Rightarrow 4\\log_{10}3\\fallingdotseq 1.9 \\Rightarrow \\log_{10}3\\fallingdotseq\\displaystyle\\frac{1.9}{4}=0.475$\n<\/div>\n<p>$\\log_{10}4\\fallingdotseq 0.6$<\/p>\n<div style=\"margin-left: 20px;\">\n  $\\log_{10}4=\\log_{10}2^2=2\\log_{10}2\\fallingdotseq 2\\cdot0.3=0.6$\n<\/div>\n<p>$\\log_{10}5\\fallingdotseq 0.7$<\/p>\n<div style=\"margin-left: 20px;\">\n  $\\log_{10}5=\\log_{10}\\displaystyle\\frac{10}{2}=\\log_{10}10-\\log_{10}2\\fallingdotseq 1-0.3 = 0.7$\n<\/div>\n<p>$\\log_{10}6\\fallingdotseq 0.775$<\/p>\n<div style=\"margin-left: 20px;\">\n  $\\log_{10}6=\\log_{10}(2\\cdot 3)=\\log_{10}2 + \\log_{10}3\\fallingdotseq 0.3 + 0.475 = 0.775$\n<\/div>\n<p>$\\log_{10}7=0.85$<\/p>\n<div style=\"margin-left: 20px;\">\n  $\\log_{10}7^2=\\log_{10}49\\fallingdotseq \\log_{10}50 = \\log_{10}(5\\cdot10) = \\log_{10}5+\\log_{10}10\\fallingdotseq 0.7+1$<br \/>\n  $\\Rightarrow 2\\log_{10}7\\fallingdotseq 1.7 \\Rightarrow \\log_{10}7\\fallingdotseq \\displaystyle\\frac{1.7}{2}=0.85$<br \/>\n  \u9ad8\u7cbe\u5ea6\u7248\uff09<br \/>\n  $\\log_{10}7^4=\\log_{10}2401\\fallingdotseq \\log_{10}2400 = \\log_{10}(24\\cdot100) = \\log_{10}8+\\log_{10}3+\\log_{10}100$<br \/>\n  $=\\log_{10}2^3+\\log_{10}3+\\log_{10}10^2=3\\log_{10}2+\\log_{10}3+2\\log_{10}10\\fallingdotseq 3\\cdot 0.3 + 0.475 + 2\\cdot 1.0=3.375$<br \/>\n  $\\Rightarrow4\\log_{10}7=3.375\\Rightarrow\\log_{10}7\\fallingdotseq 3.375\/4=0.84375\\fallingdotseq 0.844$\n<\/div>\n<p>$\\log_{10}8\\fallingdotseq 0.9$<\/p>\n<div style=\"margin-left: 20px;\">\n  $\\log_{10}8=\\log_{10}2^3=3\\log_{10}2\\fallingdotseq 3\\cdot 0.3 = 0.9$\n<\/div>\n<p>$\\log_{10}9\\fallingdotseq 0.95$<\/p>\n<div style=\"margin-left: 20px;\">\n  $\\log_{10}9=\\log_{10}3^2=2\\log_{10}3\\fallingdotseq 2\\cdot 0.475=0.95$<br \/>\n  \u9ad8\u7cbe\u5ea6\u7248\uff09<br \/>\n  $\\log_{10}9^7=\\log_{10}4782969\\fallingdotseq \\log_{10} 4800000 = \\log_{10} (6\\cdot 8\\cdot 10^5) = \\log_{10} 6 + \\log_{10} 8 + \\log_{10} 10^5$<br \/>\n  $= 0.775 + 0.9 + 5.0=6.675$<br \/>\n  $\\Rightarrow 7\\log_{10}9=6.675 \\Rightarrow \\log_{10}9 \\fallingdotseq 6.675\/7=0.9537\\cdots\\fallingdotseq 0.954$\n<\/div>\n<p>$\\log_{10}10=1, (10^1=10)$<\/p>\n<p>\u304a\u307e\u3051\uff1a$\\log_{10}11\\fallingdotseq 1.04$<\/p>\n<div style=\"margin-left: 20px;\">\n  $\\log_{10}11^5=\\log_{10}161051\\fallingdotseq \\log_{10}160000=\\log_{10}2^4\\cdot10^4=4(\\log_{10}2+\\log_{10}10)\\fallingdotseq 4(0.3+1.0)$<br \/>\n  $\\Rightarrow 5\\log_{10}11=4\\cdot1.3\\Rightarrow \\log_{10}11\\fallingdotseq \\displaystyle\\frac{4}{5}1.3=0.8\\cdot 1.3=1.04$\n<\/div>\n<p>\u3053\u306e\u8fd1\u4f3c\u3092\u30d7\u30ed\u30c3\u30c8\u3059\u308b\u3068\u4e0b\u56f3\u306e\u3088\u3046\u306b\u306a\u308b\u3002$\\log_{10}7$\u3068$\\log_{10}9$\u306f\u4ed6\u306b\u6bd4\u3079\u3066\u8aa4\u5dee\u304c\u5927\u304d\u3044\u306e\u3067\u3001\u9ad8\u7cbe\u5ea6\u7248\u3092\u8d64\u8272\u3068\u3057\u3066\u793a\u3057\u305f\u3002<\/p>\n<p><a href=\"http:\/\/mechsys.tec.u-ryukyu.ac.jp\/~oshiro\/SiteList\/wp-content\/uploads\/2020\/06\/log10-approx.svg\"><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/mechsys.tec.u-ryukyu.ac.jp\/~oshiro\/SiteList\/wp-content\/uploads\/2020\/06\/log10-approx.svg\" alt=\"\" width=\"600\" height=\"155\" class=\"aligncenter size-full wp-image-66945\" \/><\/a><\/p>\n<style type=\"text\/css\">\ntable.mytbl {text-align: center; border: solid 1px black; border-collapse: collapse;}\ntable.mytbl  th {border: solid 1px; background: #ddf;}\ntable.mytbl td {border: dashed 1px;}\n<\/style>\n<table class=\"mytbl\" style=\"\">\n<tr>\n<th><\/th>\n<th>1<\/th>\n<th>2<\/th>\n<th>3<\/th>\n<th>4<\/th>\n<th>5<\/th>\n<th>6<\/th>\n<th>7<\/th>\n<th>8<\/th>\n<th>9<\/th>\n<th>10<\/th>\n<\/tr>\n<tr>\n<th>\u8fd1\u4f3c\u5024<\/th>\n<td>0<\/td>\n<td>0.3<\/td>\n<td>0.475<\/td>\n<td>0.6<\/td>\n<td>0.7<\/td>\n<td>0.775<\/td>\n<td>0.85<\/td>\n<td>0.9<\/td>\n<td>0.95<\/td>\n<td>1<\/td>\n<\/tr>\n<tr>\n<th>\u771f\u5024<\/th>\n<td>0.000<\/td>\n<td>0.3010<\/td>\n<td>0.4771<\/td>\n<td>0.6021<\/td>\n<td>0.6990<\/td>\n<td>0.7782<\/td>\n<td>0.8451<\/td>\n<td>0.9031<\/td>\n<td>0.9542<\/td>\n<td>1.000<\/td>\n<\/tr>\n<tr>\n<th>\u8aa4\u5dee<\/th>\n<td>0<\/td>\n<td>0.0010<\/td>\n<td>0.0021<\/td>\n<td>0.0021<\/td>\n<td>0.0010<\/td>\n<td style=\"background:#fbb\">0.0032<\/td>\n<td style=\"background:#f88\">0.0049<\/td>\n<td style=\"background:#fbb\">0.0031<\/td>\n<td style=\"background:#f88\">0.0042<\/td>\n<td>0<\/td>\n<\/tr>\n<\/table>\n<p><h2>\u89b3\u5bdf<\/h2>\n<ul>\n<li>1\uff5e10\u3067\u3001$\\log_{10}$\u306f0\uff5e1\u306b\u306a\u308b\u3002<\/li>\n<li>3\u3067$\\log_{10}$\u306f\u7d040.45\u3067\u3001\u3056\u3063\u304f\u308a\u534a\u5206\u306b\u5230\u9054\u3059\u308b\u3002<\/li>\n<li>2\u306f$\\log_{10}$\u306f\u7d040.3\u3067\u3001$4=2^2$, $8=2^3$\u3060\u3068$\\log_{10}$\u306f\u305d\u308c\u305e\u308c2,3\u500d\u306e\u7d040.6,0.9\u3068\u306a\u308b\u30028\u306e\u969b\u306b\u65e2\u306b\u307b\u307c1\u306b\u8fd1\u3044\u3053\u3068\u306b\u6ce8\u610f\u3002\n<li>5\u306f10\/2\u3067\u3001$\\log_{10}$\u306f$1-\\log_{10}2$\u3068\u306a\u308b\u306e\u3067\u7d040.7\u30021\u306810\u306e\u4e21\u7aef\u5074\u304b\u3089\u306e\u8ddd\u96e2\u3067\u3044\u3046\u30682\u306e\u5834\u5408\u3068\u540c\u3058\u3067\u7d040.3\u3002\n<li>\u500d\u306b\u306a\u308b\u3068\u3001\u5bfe\u6570\u3067\u306f\u540c\u3058\u3060\u3051\u5897\u52a0\u3059\u308b\u3002<br \/>\n\u4f8b\uff09<br \/>\n$\\log_{10}2=0.3\\stackrel{\\times 2}{\\longrightarrow}\\log_{10}4=0.6\\stackrel{\\times 2}{\\longrightarrow}\\log_{10}8=0.9$,<br \/>\n$\\log_{10}3=0.475\\stackrel{\\times 3}{\\longrightarrow}\\log_{10}9=0.95$,<br \/>\n$\\log_{10}5=0.7\\stackrel{\\times 2}{\\longrightarrow}\\log_{10}10=1.0$<br \/>\n$\\log aM=\\log a + \\log M$\u3088\u308a\u3001$a$\u500d\u3055\u308c\u3066\u3044\u308c\u3070\u3001$\\log a$\u5206\u3060\u3051\u5897\u52a0\u3059\u308b\uff08\u5272\u308c\u3070$\\log a$\u3060\u3051\u6e1b\u5c11\u3059\u308b\uff09\u3002$\\rightarrow$\u639b\u3051\u7b97\u30fb\u5272\u308a\u7b97\u304c\u540c\u3058\u8ddd\u96e2\u306e\u5909\u5316\u306b\u306a\u308b\u3002<\/p>\n<li>\n2\u3067\u5272\u308b\u3068$\\log_{10}$\u3067\u306f0.3\u6e1b\u5c11\u3059\u308b\u306e\u3067\u3001\u3053\u308c\u3092\u7528\u3044\u308b\u3068<\/p>\n<div style=\"margin-left: 20px;\">\n$\\log_{10}3\/2(=\\log_{10}1.5)\\fallingdotseq 0.475-0.3=0.175$<br \/>\n$\\log_{10}5\/2(=\\log_{10}2.5)\\fallingdotseq 0.7-0.3=0.4$<br \/>\n$\\log_{10}7\/2(=\\log_{10}3.5)\\fallingdotseq 0.85-0.3=0.55$<br \/>\n$\\log_{10}9\/2(=\\log_{10}4.5)\\fallingdotseq 0.95-0.3=0.65$\n<\/div>\n<p>\u3068\u306a\u308b\u30021\/2\u3082\u6c42\u3081\u3066\u307f\u308b\u3068\u3001<\/p>\n<div style=\"margin-left: 20px;\">\n$\\log_{10}1\/2(=\\log_{10}0.5)\\fallingdotseq 0-0.3=-0.3$\n<\/div>\n<p>\u3068\u306a\u308b\u3002<\/p>\n<div style=\"margin-left: 20px;\">\n$\\log_{10}0.5=\\log_{10}\\displaystyle\\frac{5}{10}=\\log_{10}5-\\log_{10}10\\fallingdotseq 0.7-1=-0.3$\n<\/div>\n<p>\u3067\u3082\u7d50\u679c\u306f\u540c\u69d8\u3002\n<\/ul>\n<h3>\u53c2\u8003\u30ea\u30f3\u30af<\/h3>\n<ul>\n<li><a href=\"https:\/\/mathtrain.jp\/log10e\">\u5e38\u7528\u5bfe\u6570\u306e\u899a\u3048\u65b9\u3068\u691c\u7b97\u3078\u306e\u5fdc\u7528 | \u9ad8\u6821\u6570\u5b66\u306e\u7f8e\u3057\u3044\u7269\u8a9e<br \/>\n<\/a><\/p>\n<li><a href=\"https:\/\/mathtrain.jp\/logseisitsu\">\u5bfe\u6570\u306e\u57fa\u672c\u7684\u306a\u6027\u8cea\u3068\u305d\u306e\u8a3c\u660e | \u9ad8\u6821\u6570\u5b66\u306e\u7f8e\u3057\u3044\u7269\u8a9e<br \/>\n<\/a><\/p>\n<li><a href=\"https:\/\/math.nakaken88.com\/textbook\/basic-logarithm-of-product-and-power\/\">\u3010\u57fa\u672c\u3011\u5bfe\u6570\u306e\u6027\u8cea\uff08\u7a4d\u3084\u7d2f\u4e57\u306e\u5bfe\u6570\uff09 | \u306a\u304b\u3051\u3093\u306e\u6570\u5b66\u30ce\u30fc\u30c8<br \/>\n<\/a><\/p>\n<li><a href=\"https:\/\/examist.jp\/mathematics\/exp-log\/log-teigi-kousiki\/\">\u3010\u9ad8\u6821\u6570\u5b66\u2161\u3011\u5bfe\u6570\u306e\u5b9a\u7fa9\u3001\u5bfe\u6570\u306e\u6027\u8cea\u30fb\u5e95\u306e\u5909\u63db\u516c\u5f0f\u30fb\u88cf\u6280\u516c\u5f0f\u306e\u8a3c\u660e | \u53d7\u9a13\u306e\u6708<br \/>\n<\/a><\/p>\n<li><a href=\"http:\/\/kou.benesse.co.jp\/nigate\/math\/a13m1203.html\">\u5bfe\u6570\u306e\u6027\u8cea\u304c\u6210\u308a\u7acb\u3064\u7406\u7531\uff5c\u6570\u5b66\uff5c\u82e6\u624b\u89e3\u6c7aQ&#038;A\uff5c\u9032\u7814\u30bc\u30df\u9ad8\u6821\u8b1b\u5ea7\uff5c\u30d9\u30cd\u30c3\u30bb\u30b3\u30fc\u30dd\u30ec\u30fc\u30b7\u30e7\u30f3<br \/>\n<\/a><\/p>\n<li><a href=\"https:\/\/www.chart.co.jp\/subject\/sugaku\/suken_tsushin\/91\/91-7.pdf\">\u5e38\u7528\u5bfe\u6570log_10 7 \u306e\u8fd1\u4f3c\u5024\u306b\u95a2\u3059\u308b\u4e00\u8003\u5bdf\uff08\u7d50\u5ddd\uff20\u8c4a\u5ca1\u9ad8\uff09 \u6570\u7814\u51fa\u7248<br \/>\n<\/a><\/p>\n<li><a href=\"https:\/\/detail.chiebukuro.yahoo.co.jp\/qa\/question_detail\/q14110888614\">\u5e38\u7528\u5bfe\u6570\u306b\u3064\u3044\u3066 &#8211; \u5e38\u7528\u5bfe\u6570\u3092\u95a2\u6570\u96fb\u5353\u3092\u4f7f\u308f\u305a\u306b\u6b63\u78ba\u306b\u8a08\u7b97\u3059\u308b\u65b9\u6cd5&#8230; &#8211; Yahoo!\u77e5\u6075\u888b<br \/>\n<\/a><\/p>\n<li><a href=\"https:\/\/detail.chiebukuro.yahoo.co.jp\/qa\/question_detail\/q1325670013\">log[10]2\u306e\u6c42\u3081\u65b9 &#8211; \u5bfe\u6570\u8868\u306b\u3088\u308b\u3068\u3001log[10]2\u306f\u7d040.301\u3060\u3068\u3044\u3046\u3053&#8230; &#8211; Yahoo!\u77e5\u6075\u888b<br \/>\n<\/a><\/p>\n<li><a href=\"https:\/\/www.youtube.com\/watch?v=RfLOC-c0UPI\">\u30103\u5206\u52d5\u753b\u3011\u5e38\u7528\u5bfe\u6570\u306e\u8fd1\u4f3c\u5024\u3092\u6c42\u3081\u308b \u6570\u5b66II \u6307\u6570\u95a2\u6570\u3068\u5bfe\u6570\u95a2\u6570 &#8211; YouTube<br \/>\n<\/a><\/p>\n<li><a href=\"https:\/\/www.youtube.com\/watch?v=d6DXAHZBcbA\">\u5e38\u7528\u5bfe\u6570\u3092\u666e\u901a\u306e\u96fb\u5353\u3060\u3051\u3067\u8a08\u7b97\u3059\u308b\u65b9\u6cd5 &#8211; YouTube<br \/>\n<\/a><\/p>\n<li><a href=\"https:\/\/www.youtube.com\/watch?v=d6DXAHZBcbA\">\u30103\u5206\u52d5\u753b\u3011\u5e38\u7528\u5bfe\u6570\u306e\u8fd1\u4f3c\u5024\u3092\u6c42\u3081\u308b \u6570\u5b66II \u6307\u6570\u95a2\u6570\u3068\u5bfe\u6570\u95a2\u6570 &#8211; YouTube<br \/>\n<\/a>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>\u5bfe\u6570\u306f\u300c\u5e95$x$\u306e\u5024\u3092\u4f55\u4e57\u3057\u305f\u3089$z$\u306b\u306a\u308b\u304b\uff1f\u300d\u306e\u6307\u6570\u3092\u6c42\u3081\u308b\u3082\u306e\u3001\u6307\u5b9a\u3059\u308b\u3082\u306e\u3068\u6349\u3048\u308b\u3002 $z=x^y$\u3067\u306e$y$\u3092\u77e5\u308a\u305f\u3044\u5834\u5408\u306b$y=\\log_{x}z$\u3068\u66f8\u304f\u3002 \u5bfe\u6570\u95a2\u9023\u306e\u516c\u5f0f \u5e38\u7528\u5bfe\u6570\u306f\u3001\u5bfe\u6570\u306e\u5e95\u304c10\u306e\u3082\u306e\u3002 [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"inline_featured_image":false,"footnotes":""},"categories":[1],"tags":[455],"_links":{"self":[{"href":"http:\/\/mechsys.tec.u-ryukyu.ac.jp\/~oshiro\/SiteList\/wp-json\/wp\/v2\/posts\/64874"}],"collection":[{"href":"http:\/\/mechsys.tec.u-ryukyu.ac.jp\/~oshiro\/SiteList\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/mechsys.tec.u-ryukyu.ac.jp\/~oshiro\/SiteList\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/mechsys.tec.u-ryukyu.ac.jp\/~oshiro\/SiteList\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"http:\/\/mechsys.tec.u-ryukyu.ac.jp\/~oshiro\/SiteList\/wp-json\/wp\/v2\/comments?post=64874"}],"version-history":[{"count":27,"href":"http:\/\/mechsys.tec.u-ryukyu.ac.jp\/~oshiro\/SiteList\/wp-json\/wp\/v2\/posts\/64874\/revisions"}],"predecessor-version":[{"id":67398,"href":"http:\/\/mechsys.tec.u-ryukyu.ac.jp\/~oshiro\/SiteList\/wp-json\/wp\/v2\/posts\/64874\/revisions\/67398"}],"wp:attachment":[{"href":"http:\/\/mechsys.tec.u-ryukyu.ac.jp\/~oshiro\/SiteList\/wp-json\/wp\/v2\/media?parent=64874"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/mechsys.tec.u-ryukyu.ac.jp\/~oshiro\/SiteList\/wp-json\/wp\/v2\/categories?post=64874"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/mechsys.tec.u-ryukyu.ac.jp\/~oshiro\/SiteList\/wp-json\/wp\/v2\/tags?post=64874"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}