{"id":150096,"date":"2020-04-02T00:02:48","date_gmt":"2020-04-02T03:02:48","guid":{"rendered":"http:\/\/clubes.obmep.org.br\/blog\/?page_id=150096"},"modified":"2023-06-11T01:04:59","modified_gmt":"2023-06-11T04:04:59","slug":"problema-qual-a-maior-potencia","status":"publish","type":"page","link":"https:\/\/clubes.obmep.org.br\/blog\/problema-qual-a-maior-potencia\/","title":{"rendered":".Problema: Qual a maior pot\u00eancia?"},"content":{"rendered":"<p style=\"margin:10px\">\n<div class=\"g1n\" style=\"line-height:25px;\">\n<p class=\"tit\" style=\"line-height:20px; margin-bottom: 10px;\">Problema<br \/>\n<span style=\"font-size:12px;color:#800000\"> (Indicado a partir do 7\u00ba ano do E. F.)<\/span><\/p>\n<hr style=\"height:1px; width:100%;background-color:#800000; margin-top: 10px; margin-bottom: 20px;border: 0 none\"\/>\n<p>Qual dos n\u00fameros \u00e9 maior: [tex]31^{11}[\/tex] ou [tex]17^{14}[\/tex]?<\/p>\n<p style=\"margin:10px\">\n<\/div>\n<p style=\"margin:40px\">\n<div class=\"g1n\" style=\"line-height:30px;\">\n<p class=\"tit\" style=\"line-height:30px; margin-bottom: 10px;\">Solu\u00e7\u00e3o<\/p>\n<hr style=\"height:1px; width:100%;background-color:#800000; margin-top: 10px; margin-bottom: 20px;border: 0 none\"\/>\n<p>Repare que, como [tex]17 \\gt 16[\/tex], temos:<\/p>\n<ul>\n<li>[tex]17^{14}\\gt 16^{14}= (2^{4})^{14}=2^{56}\\qquad \\textcolor{#800000}{(i)}[\/tex].<\/li>\n<\/ul>\n<p>Mas tamb\u00e9m [tex]31 \\lt 32[\/tex], logo:<\/p>\n<ul>\n<li>[tex]31^{11}\\lt 32^{11} = (2^{5})^{11}=2^{55}\\qquad \\textcolor{#800000}{(ii)}[\/tex].<\/li>\n<\/ul>\n<p>Como [tex]2^{56}\\gt 2^{55}[\/tex], segue de [tex]\\textcolor{#800000}{(i)}[\/tex] e de [tex]\\textcolor{#800000}{(ii)}[\/tex] que:<br \/>\n[tex] \\qquad 17^{14}\\gt 2^{56} \\gt 2^{55} \\gt 31^{11}[\/tex].<br \/>\nPortanto,  [tex]\\fcolorbox{black}{#eee0e5}{$17^{14} $}\\,[\/tex] \u00e9 o maior.<\/p>\n<hr style=\"height:1px; width:100%;background-color:#800000; margin-top: 10px; margin-bottom: 15px;border: 0 none\"\/>\n<p class=\"g2\" style=\"line-height:20px;\">Solu\u00e7\u00e3o elaborada pelos <strong>Moderadores do Blog<\/strong>.<\/p>\n<\/div>\n<p style=\"margin:10px\">\n","protected":false},"excerpt":{"rendered":"<p>Problema (Indicado a partir do 7\u00ba ano do E. F.) Qual dos n\u00fameros \u00e9 maior: [tex]31^{11}[\/tex] ou [tex]17^{14}[\/tex]? Solu\u00e7\u00e3o Repare que, como [tex]17 \\gt 16[\/tex], temos: [tex]17^{14}\\gt 16^{14}= (2^{4})^{14}=2^{56}\\qquad \\textcolor{#800000}{(i)}[\/tex]. Mas tamb\u00e9m [tex]31 \\lt 32[\/tex], logo: [tex]31^{11}\\lt 32^{11} = (2^{5})^{11}=2^{55}\\qquad \\textcolor{#800000}{(ii)}[\/tex]. Como [tex]2^{56}\\gt 2^{55}[\/tex], segue de [tex]\\textcolor{#800000}{(i)}[\/tex] e de [tex]\\textcolor{#800000}{(ii)}[\/tex] que: [tex] \\qquad 17^{14}\\gt 2^{56} &hellip; <\/p>\n<p><a class=\"more-link btn\" href=\"https:\/\/clubes.obmep.org.br\/blog\/problema-qual-a-maior-potencia\/\">Continue lendo<\/a><\/p>\n","protected":false},"author":668,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"template-onecolumn.php","meta":{"footnotes":""},"class_list":["post-150096","page","type-page","status-publish","hentry","nodate","item-wrap"],"_links":{"self":[{"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/pages\/150096","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/users\/668"}],"replies":[{"embeddable":true,"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/comments?post=150096"}],"version-history":[{"count":12,"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/pages\/150096\/revisions"}],"predecessor-version":[{"id":194285,"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/pages\/150096\/revisions\/194285"}],"wp:attachment":[{"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/media?parent=150096"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}