{"id":1432,"date":"2025-07-19T17:11:41","date_gmt":"2025-07-19T08:11:41","guid":{"rendered":"https:\/\/math-friend.com\/?p=1432"},"modified":"2025-08-01T09:53:08","modified_gmt":"2025-08-01T00:53:08","slug":"%e3%80%90%e5%8c%97%e6%b5%b7%e9%81%93%e5%a4%a7%e5%ad%a6%e5%85%a5%e8%a9%a6%e3%80%91%e6%9d%a1%e4%bb%b6%e3%81%8b%e3%82%89%e9%96%a2%e6%95%b0%e3%81%ae%e5%bd%a2%e3%82%92%e6%b1%ba%e5%ae%9a%e3%81%99%e3%82%8b","status":"publish","type":"post","link":"https:\/\/math-friend.com\/?p=1432","title":{"rendered":"\u3010\u5317\u6d77\u9053\u5927\u5b66\u5165\u8a66\u3011\u6761\u4ef6\u304b\u3089\u95a2\u6570\u306e\u5f62\u3092\u6c7a\u5b9a\u3059\u308b\u554f\u984c(2025)"},"content":{"rendered":"\n<p>\u4eca\u56de\u306f\u3053\u3061\u3089\u306e\u554f\u984c\u3092\u89e3\u3044\u3066\u3044\u304d\u307e\u3059.<\/p>\n\n\n\n<p class=\"has-border -border02\">\u3059\u3079\u3066\u306e\u5b9f\u6570\\(x\\)\u3067\u5b9a\u7fa9\u3055\u308c\u305f\u95a2\u6570\\(f(x)\\)\u306f\u3059\u3079\u3066\u306e\u6574\u6570\\(n\\)\u306b\u5bfe\u3057\u3066,<br>$$<br>f(nx)=\\left\\{f(x)\\right\\}^n<br>$$\u304c\u6210\u308a\u7acb\u3061, \u3055\u3089\u306b\\(f(1)=2\\)\u3067\u3042\u308b. \u305f\u3060\u3057, \\(f(x)\\)\u306e\u3068\u308a\u3046\u308b\u5024\u306f\\(0\\)\u3092\u9664\u304f\u5b9f\u6570\u3068\u3059\u308b. <br>\u3053\u306e\u3068\u304d, \u4ee5\u4e0b\u306e\u554f\u3044\u306b\u7b54\u3048\u3088.<br><br>(1) \\(f(n)&lt;100\\)\u3092\u6e80\u305f\u3059\u6700\u5927\u306e\u6574\u6570\\(n\\)\u3092\u6c42\u3081\u3088.<br>(2) \u3059\u3079\u3066\u306e\u5b9f\u6570\\(x\\)\u306b\u5bfe\u3057\u3066, \\(f(x)&gt;0\\)\u3067\u3042\u308b\u3053\u3068\u3092\u8a3c\u660e\u305b\u3088.<br>(3) \\(f(0.25)\\)\u306e\u5024\u3092\u6c42\u3081\u3088.<br>(4) \\(a\\)\u304c\u6709\u7406\u6570\u306e\u3068\u304d, \\(f(a)\\)\u3092\\(a\\)\u306e\u5f0f\u3067\u8868\u305b.<br><span style=\"text-align:right;display:block;\">(2025 \u5317\u6d77\u9053\u5927\u5b66 \u6587\u7cfb[4])<\/span><\/p>\n\n\n\n<p>\u3053\u3061\u3089\u306e\u554f\u984c\u306f\u9ad8\u6821\u6570\u5b66\u306e\u30c6\u30ad\u30b9\u30c8, \u554f\u984c\u96c6\u3067\u306f\u3042\u307e\u308a\u898b\u304b\u3051\u306a\u3044\u30bf\u30a4\u30d7\u306e\u554f\u984c\u3067\u3059. \u30d1\u30ba\u30eb\u306e\u3088\u3046\u306a\u611f\u3058\u3067, \u89e3\u6cd5\u306e\u30a2\u30a4\u30c7\u30a3\u30a2\u304c\u601d\u3044\u3064\u3051\u3070\u7c21\u5358\u306b\u89e3\u3051, \u601d\u3044\u3064\u304b\u306a\u304b\u3063\u305f\u3089\u89e3\u304f\u3053\u3068\u304c\u96e3\u3057\u3044\u3067\u3059. <br><br>\u95a2\u6570\u306e\u5f62\u3092\u6c7a\u5b9a\u3059\u308b\u554f\u984c\u3067\u3059\u304c, \u809d\u3068\u306a\u308b\u306e\u306f, <br>$$<br>f(nx)=\\left\\{f(x)\\right\\}^n<br>$$\u306e\u95a2\u4fc2\u5f0f\u3067\u3059. \u3053\u306e\u5f62\u304b\u3089, \u6307\u6570\u95a2\u6570\u3092\u601d\u3044\u4ed8\u304d\u307e\u3059. \u5b9f\u969b, \u6307\u6570\u95a2\u6570\\( \\displaystyle f(x)=a^x\\)\u306f, \\( \\displaystyle f(nx)=a^{nx}=(a^x)^n=\\left\\{f(x)\\right\\}^n\\)\u3092\u6e80\u305f\u3057\u3044\u307e\u3059. \u305d\u3057\u3066, \\(f(1)=2\\)\u3067\u3042\u308b\u3053\u3068\u304b\u3089, \\(f(x)=2^x\\)\u306b\u306a\u308b\u3068\u4e88\u60f3\u3067\u304d\u307e\u3059. \u305d\u3057\u3066\u3053\u306e\u4e88\u60f3\u306f\u534a\u5206\u6b63\u3057\u3044\u3067\u3059. \u89e3\u7b54\u306e\u5f8c\u306b\u3053\u3061\u3089\u306b\u3064\u3044\u3066\u88dc\u8db3\u3057\u307e\u3059\u304c, \u3053\u306e\u3088\u3046\u306b\u95a2\u6570\u306e\u5f62\u3092\u3042\u308b\u7a0b\u5ea6\u4e88\u60f3\u3057\u3066\u304a\u304f\u3068\u89e3\u304d\u3084\u3059\u3044\u304b\u3068\u601d\u3044\u307e\u3059.<br><br>\u305d\u308c\u3067\u306f\u89e3\u3044\u3066\u3044\u304d\u307e\u3057\u3087\u3046.<\/p>\n\n\n\n<div class=\"wp-block-group is-style-crease\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p>(1) \u6574\u6570\\(n\\)\u306b\u5bfe\u3057\u3066, <br>$$<br>f(n)=f(n\\cdot 1)=\\left\\{f(1)\\right\\}^n=2^n<br>$$\u3068\u306a\u308b\u306e\u3067, <br>$$<br>f(n)=2^n&lt;100<br>$$\u3092\u89e3\u3051\u3070\u826f\u3044. \\(2^n\\)\u306f\\(n\\)\u306b\u95a2\u3057\u3066\u5358\u8abf\u306b\u5897\u3048, \\(2^6=64&lt;100\\), \\(2^7=128&gt;100\\)\u3088\u308a, \u3053\u306e\u4e0d\u7b49\u5f0f\u3092\u6e80\u305f\u3059\u6700\u5927\u306e\u6574\u6570\u306f\\(6\\)\u3067\u3042\u308b.<\/p>\n\n\n\n<p>(2) \\(2\\)\u306f\u6574\u6570\u3060\u304b\u3089, \u5b9f\u6570\\(x\\)\u306b\u5bfe\u3057\u3066,<br>$$<br>f(x)=f\\left(2\\cdot\\frac{x}{2}\\right)=\\left\\{f\\left(\\frac{x}{2}\\right)\\right\\}^2<br>$$\u3068\u306a\u308a, \\(\\displaystyle f\\left(\\frac{x}{2}\\right)\\)\u306f\\(0\\)\u3067\u306a\u3044\u5b9f\u6570\u306a\u306e\u3067\\(2\\)\u4e57\u3059\u308b\u3068\u6b63\u3068\u306a\u308b. \u3088\u3063\u3066, <br>$$<br>f(x)=\\left\\{f\\left(\\frac{x}{2}\\right)\\right\\}^2&gt;0<br>$$\u304c\u308f\u304b\u308b.<\/p>\n\n\n\n<p>(3) \\(\\displaystyle 0.25=\\frac{1}{4}\\)\u306b\u6ce8\u610f\u3057\u3066,<br>$$<br>2=f(1)=f\\left(4\\cdot \\frac{1}{4}\\right)=\\left\\{f\\left(\\frac{1}{4}\\right)\\right\\}^4=\\left\\{f\\left(0.25\\right)\\right\\}^4<br>$$\u3067\u3042\u308b\u304b\u3089, \\(f(0.25)\\)\u306f\\(4\\)\u4e57\u3059\u308b\u3068\\(2\\)\u306b\u306a\u308b\u5b9f\u6570\u3067\u3042\u308b. \u305d\u3057\u3066(2)\u3088\u308a\\(f(0.25)&gt;0\\)\u3060\u304b\u3089, <br>$$<br>f(0.25)=2^{\\frac{1}{4}}<br>$$\u304c\u308f\u304b\u308b.<\/p>\n\n\n\n<p>(4) \\(a\\)\u3092\u6709\u7406\u6570\u3068\u3059\u308b\u3068, \u6b63\u306e\u6574\u6570\\(p\\)\u3068, \u6574\u6570\\(q\\)\u304c\u5b58\u5728\u3057\u3066, <br>$$<br>a=\\frac{q}{p}<br>$$\u3068\u8868\u305b\u308b. <br>$$<br>f(q)=f(p\\cdot a)=\\left\\{f\\left(a\\right)\\right\\}^p<br>$$\u3067\u3042\u308a, (1)\u306e\u8b70\u8ad6\u3088\u308a, \u6574\u6570\\(q\\)\u306b\u5bfe\u3057\u3066\\( \\displaystyle f(q)=2^q\\)\u3067\u3042\u308b\u304b\u3089, <br>$$<br>\\left\\{f\\left(a\\right)\\right\\}^p=2^q<br>$$\u3068\u306a\u308a, (2)\u304b\u3089\\( \\displaystyle f\\left(a\\right)&gt;0\\)\u306a\u306e\u3067, <br>$$<br>f(a)=\\left(2^q\\right)^{\\frac{1}{p}}=2^{\\frac{q}{p}}=2^a<br>$$\u304c\u308f\u304b\u308b.<\/p>\n<\/div><\/div>\n\n\n\n<p>\u5f53\u521d\u4e88\u60f3\u3057\u305f\u901a\u308a, \u5c11\u306a\u304f\u3068\u3082\u6709\u7406\u6570\\(a\\)\u306b\u5bfe\u3057\u3066\u306f, \\(f(a)=2^a\\)\u304c\u308f\u304b\u308a\u307e\u3057\u305f. \u305d\u308c\u3067\u306f\u5b9f\u6570\\(x\\)\u306b\u5bfe\u3057\u3066, \\(f(x)=2^x\\)\u3068\u306a\u308b\u304b\u3068\u554f\u308f\u308c\u308c\u3070, \u7b54\u3048\u306f\u300c\u30ce\u30fc\u300d\u3067\u3059.<br><br>\u4f8b\u3048\u3070, \\(f(x)\\)\u3092<br>$$f(x)=\\left\\{<br>\\begin{array}{ll}<br>2^x &amp; (x\u304c\u6709\u7406\u6570\u306e\u6642) \\\\[1.5ex]<br>3^x &amp; (x\u304c\u7121\u7406\u6570\u306e\u6642)<br>\\end{array}<br>\\right.$$\u3067\u5b9a\u7fa9\u3059\u308b\u3068, \u3053\u308c\u306f\\(f(x)\\)\u304c\u6e80\u305f\u3059\u3079\u304d\u6761\u4ef6\u3092\u5168\u3066\u6e80\u305f\u3057\u307e\u3059. <br><br>\u5b9f\u969b, \\(f(1)=2\\), \\(f(x)>0\\)\u306f\u3059\u3050\u306b\u308f\u304b\u308a\u307e\u3059. \\(x\\)\u304c\u6709\u7406\u6570\u306e\u3068\u304d, \u6574\u6570\\(n\\)\u306b\u5bfe\u3057\u3066\\(nx\\)\u3082\u307e\u305f\u6709\u7406\u6570\u306a\u306e\u3067, <br>$$<br>f(nx)=2^{nx}=\\left(2^x\\right)^n=\\left\\{f(x)\\right\\}^n<br>$$\u3068\u306a\u308a, \u6761\u4ef6\u5f0f\u3092\u6e80\u305f\u3057\u307e\u3059. \u3055\u3089\u306b, \\(x\\)\u304c\u7121\u7406\u6570\u306e\u3068\u304d, \\(n\\)\u3092\\(0\\)\u3067\u306a\u3044\u6574\u6570\u3068\u3059\u308b\u3068, \\(nx\\)\u3082\u307e\u305f\u7121\u7406\u6570\u306a\u306e\u3067,<br>$$<br>f(nx)=3^{nx}=\\left(3^x\\right)^n=\\left\\{f(x)\\right\\}^n<br>$$\u3068\u306a\u308a, \u3053\u3061\u3089\u3082\u6761\u4ef6\u5f0f\u3092\u6e80\u305f\u3057\u307e\u3059. \u307e\u305f, \\(x\\)\u304c\u7121\u7406\u6570\u3067, \\(n=0\\)\u306e\u3068\u304d\u306f, \\(nx=0\\cdot x=0\\)\u306f\u6709\u7406\u6570\u306a\u306e\u3067, <br>$$<br>f(n\\cdot x)=f(0)=2^0=1=\\left(3^x\\right)^0=\\left\\{f(x)\\right\\}^0=\\left\\{f(x)\\right\\}^n<br>$$\u3068\u306a\u308a, \u3084\u306f\u308a\u3053\u306e\u5834\u5408\u3082\u6761\u4ef6\u5f0f\u3092\u6e80\u305f\u3057\u307e\u3059.<br><br>\u3053\u306e\u3088\u3046\u306b\u6709\u7406\u6570\\(x\\)\u306b\u5bfe\u3057\u3066\u306f, \\( \\displaystyle f(x)=2^x\\)\u304c\u78ba\u5b9a\u3057\u307e\u3059\u304c, \u7121\u7406\u6570\\(x\\)\u306b\u3064\u3044\u3066\u306f, \\(a\\)\u3092\\(0\\)\u3067\u306f\u306a\u3044\u5b9f\u6570\u3068\u3057\u3066, \\( \\displaystyle f(x)=a^x\\)\u3068\u3057\u3066\u3082\u826f\u3044\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059. \u7279\u306b\\(a=1\\)\u3068\u3059\u308c\u3070, \u7121\u7406\u6570\u306b\u5bfe\u3057\u3066\u5e38\u306b\\(1\\)\u3092\u8fd4\u3059\u95a2\u6570\u3067\u3082\u6761\u4ef6\u3092\u6e80\u305f\u3059\u3053\u3068\u304c\u308f\u304b\u308b\u306e\u3067\u3059.<br><br>\u7121\u7406\u6570\u306b\u95a2\u3057\u3066\u3082\\( \\displaystyle f(x)=2^x\\)\u304c\u78ba\u5b9a\u3059\u308b\u3088\u3046\u306b\u3057\u305f\u3044\u5834\u5408\u306f, \u300c\\(f(x)\\)\u306f\u9023\u7d9a\u95a2\u6570\u3067\u3042\u308b\u300d\u3068\u3044\u3046\u6761\u4ef6\u3092\u52a0\u3048\u308c\u3070\u826f\u3044\u3067\u3059. \u3053\u306e\u8fba\u308a\u306f\u5927\u5b66\u306e\u5fae\u7a4d\u306e\u6388\u696d\u3067, \u6307\u6570\u95a2\u6570\u3092\u53b3\u5bc6\u306b\u5b9a\u7fa9\u3059\u308b\u969b\u306b\u8a73\u3057\u304f\u5b66\u3073\u307e\u3059.<\/p>\n\n\n\n<p>youtube\u3067\u3082\u89e3\u8aac\u3057\u3066\u3044\u307e\u3059.<\/p>\n\n\n\n<iframe width=\"560\" height=\"315\" src=\"https:\/\/www.youtube.com\/embed\/j5bSkPbjmfA?si=9eSPoO-Y4Fi9hf_W\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe>\n\n\n\n\n","protected":false},"excerpt":{"rendered":"<p>\u4eca\u56de\u306f\u3053\u3061\u3089\u306e\u554f\u984c\u3092\u89e3\u3044\u3066\u3044\u304d\u307e\u3059. \u3059\u3079\u3066\u306e\u5b9f\u6570\\(x\\)\u3067\u5b9a\u7fa9\u3055\u308c\u305f\u95a2\u6570\\(f(x)\\)\u306f\u3059\u3079\u3066\u306e\u6574\u6570\\(n\\)\u306b\u5bfe\u3057\u3066,$$f(nx)=\\left\\{f(x)\\right\\}^n$$\u304c\u6210\u308a\u7acb\u3061, \u3055\u3089\u306b\\(f(1) [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":1463,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"swell_btn_cv_data":"","_themeisle_gutenberg_block_has_review":false,"footnotes":""},"categories":[6],"tags":[],"class_list":["post-1432","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-tokimakuru"],"_links":{"self":[{"href":"https:\/\/math-friend.com\/index.php?rest_route=\/wp\/v2\/posts\/1432","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/math-friend.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/math-friend.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/math-friend.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/math-friend.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1432"}],"version-history":[{"count":35,"href":"https:\/\/math-friend.com\/index.php?rest_route=\/wp\/v2\/posts\/1432\/revisions"}],"predecessor-version":[{"id":2213,"href":"https:\/\/math-friend.com\/index.php?rest_route=\/wp\/v2\/posts\/1432\/revisions\/2213"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/math-friend.com\/index.php?rest_route=\/wp\/v2\/media\/1463"}],"wp:attachment":[{"href":"https:\/\/math-friend.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1432"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/math-friend.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1432"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/math-friend.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1432"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}