{"id":7323,"date":"2012-01-16T22:39:48","date_gmt":"2012-01-16T22:39:48","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=7323"},"modified":"2021-12-30T19:22:08","modified_gmt":"2021-12-30T19:22:08","slug":"simplifique-as-expressoes","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=7323","title":{"rendered":"Simplifique as express\u00f5es"},"content":{"rendered":"<p><ul id='GTTabs_ul_7323' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_7323' class='GTTabs_curr'><a  id=\"7323_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_7323' ><a  id=\"7323_1\" onMouseOver=\"GTTabsShowLinks('R1'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>R1<\/a><\/li>\n<li id='GTTabs_li_2_7323' ><a  id=\"7323_2\" onMouseOver=\"GTTabsShowLinks('R2'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>R2<\/a><\/li>\n<li id='GTTabs_li_3_7323' ><a  id=\"7323_3\" onMouseOver=\"GTTabsShowLinks('R3'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>R3<\/a><\/li>\n<li id='GTTabs_li_4_7323' ><a  id=\"7323_4\" onMouseOver=\"GTTabsShowLinks('R4'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>R4<\/a><\/li>\n<li id='GTTabs_li_5_7323' ><a  id=\"7323_5\" onMouseOver=\"GTTabsShowLinks('R5'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>R5<\/a><\/li>\n<\/ul>\n\n<div class='GTTabs_divs GTTabs_curr_div' id='GTTabs_0_7323'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Simplifique as express\u00f5es:<\/p>\n<ul>\n<li>$A=\\ln e+\\ln {{e}^{2}}+\\ln {{e}^{3}}$<\/li>\n<li>$B=\\ln e-\\ln \\left( \\frac{1}{e} \\right)$<\/li>\n<li>$C=\\ln \\left( e\\sqrt{2} \\right)$<\/li>\n<li>$D=\\ln {{e}^{2}}-2\\ln e$<\/li>\n<li>$E=\\ln 3+\\ln \\left( 27e \\right)-\\ln \\left( 9{{e}^{3}} \\right)$<\/li>\n<\/ul>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_7323' onClick='GTTabs_show(1,7323)'>R1 &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_7323'>\n<span class='GTTabs_titles'><b>R1<\/b><\/span><!--more--><\/p>\n<p>\\[\\begin{array}{*{35}{l}}<br \/>\nA &amp; = &amp; \\ln e+\\ln {{e}^{2}}+\\ln {{e}^{3}}\u00a0 \\\\<br \/>\n{} &amp; = &amp; 1+2+3\u00a0 \\\\<br \/>\n{} &amp; = &amp; 6\u00a0 \\\\<br \/>\n\\end{array}\\]<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_7323' onClick='GTTabs_show(0,7323)'>&lt;&lt; Enunciado<\/a><\/span><span class='GTTabs_nav_next'><a href='#GTTabs_ul_7323' onClick='GTTabs_show(2,7323)'>R2 &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_2_7323'>\n<span class='GTTabs_titles'><b>R2<\/b><\/span><\/p>\n<p>\\[\\begin{array}{*{35}{l}}<br \/>\nB &amp; = &amp; \\ln e-\\ln \\left( \\frac{1}{e} \\right)\u00a0 \\\\<br \/>\n{} &amp; = &amp; 1-\\ln \\left( {{e}^{-1}} \\right)\u00a0 \\\\<br \/>\n{} &amp; = &amp; 1-(-1)\u00a0 \\\\<br \/>\n{} &amp; = &amp; 2\u00a0 \\\\<br \/>\n\\end{array}\\]<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_7323' onClick='GTTabs_show(1,7323)'>&lt;&lt; R1<\/a><\/span><span class='GTTabs_nav_next'><a href='#GTTabs_ul_7323' onClick='GTTabs_show(3,7323)'>R3 &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_3_7323'>\n<span class='GTTabs_titles'><b>R3<\/b><\/span><\/p>\n<p>\\[\\begin{array}{*{35}{l}}<br \/>\nC &amp; = &amp; \\ln \\left( e\\sqrt{2} \\right)\u00a0 \\\\<br \/>\n{} &amp; = &amp; \\ln e+\\ln \\sqrt{2}\u00a0 \\\\<br \/>\n{} &amp; = &amp; 1+\\ln {{2}^{\\frac{1}{2}}}\u00a0 \\\\<br \/>\n{} &amp; = &amp; 1+\\frac{1}{2}\\ln 2\u00a0 \\\\<br \/>\n\\end{array}\\]<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_7323' onClick='GTTabs_show(2,7323)'>&lt;&lt; R2<\/a><\/span><span class='GTTabs_nav_next'><a href='#GTTabs_ul_7323' onClick='GTTabs_show(4,7323)'>R4 &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_4_7323'>\n<span class='GTTabs_titles'><b>R4<\/b><\/span><\/p>\n<p>\\[\\begin{array}{*{35}{l}}<br \/>\nD &amp; = &amp; \\ln {{e}^{2}}-2\\ln e\u00a0 \\\\<br \/>\n{} &amp; = &amp; 2-2\\times 1\u00a0 \\\\<br \/>\n{} &amp; = &amp; 0\u00a0 \\\\<br \/>\n\\end{array}\\]<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_7323' onClick='GTTabs_show(3,7323)'>&lt;&lt; R3<\/a><\/span><span class='GTTabs_nav_next'><a href='#GTTabs_ul_7323' onClick='GTTabs_show(5,7323)'>R5 &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_5_7323'>\n<span class='GTTabs_titles'><b>R5<\/b><\/span><\/p>\n<p>\\[\\begin{array}{*{35}{l}}<br \/>\nE &amp; = &amp; \\ln 3+\\ln \\left( 27e \\right)-\\ln \\left( 9{{e}^{3}} \\right)\u00a0 \\\\<br \/>\n{} &amp; = &amp; \\ln 3+\\ln \\left( \\frac{27e}{9{{e}^{3}}} \\right)\u00a0 \\\\<br \/>\n{} &amp; = &amp; \\ln 3+\\ln \\left( \\frac{3}{{{e}^{2}}} \\right)\u00a0 \\\\<br \/>\n{} &amp; = &amp; \\ln 3+\\ln 3-\\ln {{e}^{2}}\u00a0 \\\\<br \/>\n{} &amp; = &amp; -2+2\\ln 3\u00a0 \\\\<br \/>\n\\end{array}\\]<\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_7323' onClick='GTTabs_show(4,7323)'>&lt;&lt; R4<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado R1 Enunciado Simplifique as express\u00f5es: $A=\\ln e+\\ln {{e}^{2}}+\\ln {{e}^{3}}$ $B=\\ln e-\\ln \\left( \\frac{1}{e} \\right)$ $C=\\ln \\left( e\\sqrt{2} \\right)$ $D=\\ln {{e}^{2}}-2\\ln e$ $E=\\ln 3+\\ln \\left( 27e \\right)-\\ln \\left( 9{{e}^{3}} \\right)$ R1 &gt;&gt; R1 &lt;&lt;&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":19694,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[226,97,267],"tags":[427,275,274],"series":[],"class_list":["post-7323","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-12--ano","category-aplicando","category-funcoes-exponenciais-e-logaritmicas","tag-12-o-ano","tag-funcao-logaritmica","tag-regras-operatorias-de-logaritmos"],"views":4034,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2021\/12\/Mat257.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/7323","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=7323"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/7323\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/19694"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=7323"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=7323"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=7323"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=7323"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}