{"id":3376,"date":"2021-05-17T08:12:25","date_gmt":"2021-05-17T06:12:25","guid":{"rendered":"http:\/\/jhmaths.fr\/?page_id=3376"},"modified":"2021-05-18T17:00:34","modified_gmt":"2021-05-18T15:00:34","slug":"logarithme","status":"publish","type":"page","link":"https:\/\/jhmaths.fr\/index.php\/terminale-technologique\/logarithme\/","title":{"rendered":"Logarithme d\u00e9cimal"},"content":{"rendered":"<p>[vc_row][vc_column][vc_column_text el_id=\u00a0\u00bbobjectif-1&Prime;]<\/p>\n<h1 style=\"text-align: center;\">D\u00e9finition<\/h1>\n<p>[\/vc_column_text][\/vc_column][\/vc_row][vc_row content_placement=\u00a0\u00bbmiddle\u00a0\u00bb][vc_column][vc_column_text el_class=\u00a0\u00bbproprietepremieresthr propriete\u00a0\u00bb]<b>Pour un nombre \\(b\\) positif, on appelle logarithme d\u00e9cimal de \\(b\\) la solution (unique) de l&rsquo;\u00e9quation \\(10^x=b\\).<\/b><\/p>\n<p>Graphiquement, on r\u00e9sout cette \u00e9quation en tra\u00e7ant la fonction exponentielle de base 10 et en d\u00e9terminant l&rsquo;ant\u00e9c\u00e9dent de \\(b\\).<\/p>\n<p>&nbsp;<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-3377 size-full\" src=\"https:\/\/jhmaths.fr\/wp-content\/uploads\/2021\/05\/definition.jpg\" alt=\"\" width=\"446\" height=\"378\" srcset=\"https:\/\/jhmaths.fr\/wp-content\/uploads\/2021\/05\/definition.jpg 446w, https:\/\/jhmaths.fr\/wp-content\/uploads\/2021\/05\/definition-300x254.jpg 300w\" sizes=\"auto, (max-width: 446px) 100vw, 446px\" \/>[\/vc_column_text][vc_column_text el_id=\u00a0\u00bbobjectif-2&Prime;]<\/p>\n<h1 style=\"text-align: center;\">Fonction log<\/h1>\n<p>[\/vc_column_text][vc_column_text el_class=\u00a0\u00bbproprietepremieresthr propriete\u00a0\u00bb]<b>Pour tout nombre r\u00e9el \\(x\\) , on d\u00e9finit la fonction \\( x \\mapsto log~x\\).<\/b><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-3378 size-large\" src=\"https:\/\/jhmaths.fr\/wp-content\/uploads\/2021\/05\/fonction-1024x476.jpg\" alt=\"\" width=\"945\" height=\"439\" srcset=\"https:\/\/jhmaths.fr\/wp-content\/uploads\/2021\/05\/fonction-1024x476.jpg 1024w, https:\/\/jhmaths.fr\/wp-content\/uploads\/2021\/05\/fonction-300x139.jpg 300w, https:\/\/jhmaths.fr\/wp-content\/uploads\/2021\/05\/fonction-768x357.jpg 768w, https:\/\/jhmaths.fr\/wp-content\/uploads\/2021\/05\/fonction-806x375.jpg 806w, https:\/\/jhmaths.fr\/wp-content\/uploads\/2021\/05\/fonction-558x259.jpg 558w, https:\/\/jhmaths.fr\/wp-content\/uploads\/2021\/05\/fonction-655x304.jpg 655w, https:\/\/jhmaths.fr\/wp-content\/uploads\/2021\/05\/fonction-820x381.jpg 820w, https:\/\/jhmaths.fr\/wp-content\/uploads\/2021\/05\/fonction.jpg 1067w\" sizes=\"auto, (max-width: 945px) 100vw, 945px\" \/>[\/vc_column_text][\/vc_column][\/vc_row][vc_row][vc_column][vc_column_text el_id=\u00a0\u00bbobjectif-2&Prime;]<\/p>\n<h1 style=\"text-align: center;\">Variations et signe<\/h1>\n<p>[\/vc_column_text][vc_column_text el_class=\u00a0\u00bbproprietepremieresthr propriete\u00a0\u00bb]La fonction \\( x \\mapsto log~x\\) est d\u00e9finie sur \\([0;+\\infty[\\).<\/p>\n<p>Elle est croissante.<\/p>\n<p>Elle est n\u00e9gative pour \\( 0 &lt; x &lt; 1 \\), elle vaut 0 pour \\(x=1\\) et elle est positive pour \\(x &gt;1\\).[\/vc_column_text][\/vc_column][\/vc_row][vc_row][vc_column][vc_column_text el_id=\u00a0\u00bbobjectif-3&Prime;]<\/p>\n<h1 style=\"text-align: center;\">Propri\u00e9t\u00e9s alg\u00e9briques<\/h1>\n<p>[\/vc_column_text][\/vc_column][\/vc_row][vc_row content_placement=\u00a0\u00bbmiddle\u00a0\u00bb][vc_column width=\u00a0\u00bb1\/2&Prime;][vc_column_text el_class=\u00a0\u00bbproprietepremieresthr propriete\u00a0\u00bb]Pour tout nombre \\(a\\) positif, pour tous nombres \\(x\\) et \\(y\\) r\u00e9els,<\/p>\n<ul>\n<li>\\(log (1)=0\\)<\/li>\n<li>\\(log (x \\times y)=log (x) + log (y)\\)<\/li>\n<li>\\(log \\left(\\displaystyle \\frac{x}{y}\\right)=log (x) &#8211; log (y)\\)<\/li>\n<li>\\(log (x^n)=n \\times log (x)\\)<\/li>\n<\/ul>\n<p>[\/vc_column_text][\/vc_column][vc_column width=\u00a0\u00bb1\/2&Prime;][vc_column_text]<\/p>\n<div style=\"text-align: center;\"><iframe loading=\"lazy\" src=\"https:\/\/www.youtube.com\/embed\/qdYQQlbz-AQ\" width=\"320\" height=\"180\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/div>\n<p>[\/vc_column_text][\/vc_column][\/vc_row][vc_row][vc_column][vc_column_text]<\/p>\n<h1 style=\"text-align: center;\">R\u00e9solutions d&rsquo;\u00e9quations et in\u00e9quations<\/h1>\n<p>[\/vc_column_text][\/vc_column][\/vc_row][vc_row content_placement=\u00a0\u00bbmiddle\u00a0\u00bb][vc_column][vc_column_text el_class=\u00a0\u00bbproprietepremieresthr propriete\u00a0\u00bb]Pour tous nombres \\(a\\) et \\(b\\) positifs, l&rsquo;\u00e9quation \\(a^x=b\\) a pour solution<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: center;\">\\(x=\\displaystyle \\frac{log~b}{log~a}\\)<\/p>\n<p>[\/vc_column_text][\/vc_column][\/vc_row][vc_row][vc_column][vc_column_text]<\/p>\n<h2 style=\"text-align: center;\">Plan de travail<\/h2>\n<p>[\/vc_column_text][\/vc_column][\/vc_row][vc_row][vc_column][vc_single_image source=\u00a0\u00bbexternal_link\u00a0\u00bb onclick=\u00a0\u00bbimg_link_large\u00a0\u00bb img_link_target=\u00a0\u00bb_blank\u00a0\u00bb custom_src=\u00a0\u00bbhttps:\/\/docs.google.com\/drawings\/d\/e\/2PACX-1vRcxJMMD5Hwe_z8Mg3s-NZdzFcC4ew8afZ7ecGh_HKMn4RVBwItVU4bLztZtKxrmst2WM_nut1y9qPC\/pub?w=960&amp;h=720&Prime;][\/vc_column][\/vc_row][vc_row][vc_column][vc_column_text]<\/p>\n<h2 style=\"text-align: center;\">Synth\u00e8se<\/h2>\n<p>[\/vc_column_text][\/vc_column][\/vc_row][vc_row][vc_column][vc_single_image source=\u00a0\u00bbexternal_link\u00a0\u00bb onclick=\u00a0\u00bbimg_link_large\u00a0\u00bb img_link_target=\u00a0\u00bb_blank\u00a0\u00bb custom_src=\u00a0\u00bbhttps:\/\/docs.google.com\/drawings\/d\/e\/2PACX-1vS9OE5uVVOTb3GE4ljBV62KEPVI0Qy96kSKcRMiFSGap_jzo7TnCRsTlu5i6CX_w620LU6EIJNWD_oZ\/pub?w=960&amp;h=720&Prime;][\/vc_column][\/vc_row]<\/p>\n","protected":false},"excerpt":{"rendered":"<p>[vc_row][vc_column][vc_column_text el_id=\u00a0\u00bbobjectif-1&Prime;] D\u00e9finition [\/vc_column_text][\/vc_column][\/vc_row][vc_row content_placement=\u00a0\u00bbmiddle\u00a0\u00bb][vc_column][vc_column_text el_class=\u00a0\u00bbproprietepremieresthr propriete\u00a0\u00bb]Pour un nombre \\(b\\) positif, on appelle logarithme d\u00e9cimal de \\(b\\) la solution (unique) de l&rsquo;\u00e9quation \\(10^x=b\\). Graphiquement, on r\u00e9sout cette \u00e9quation en tra\u00e7ant la fonction exponentielle de base 10 et en d\u00e9terminant l&rsquo;ant\u00e9c\u00e9dent de \\(b\\). &nbsp; [\/vc_column_text][vc_column_text el_id=\u00a0\u00bbobjectif-2&Prime;] Fonction log [\/vc_column_text][vc_column_text el_class=\u00a0\u00bbproprietepremieresthr propriete\u00a0\u00bb]Pour tout nombre r\u00e9el \\(x\\) , [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":3063,"menu_order":6,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"folder":[],"class_list":["post-3376","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/jhmaths.fr\/index.php\/wp-json\/wp\/v2\/pages\/3376","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/jhmaths.fr\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/jhmaths.fr\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/jhmaths.fr\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/jhmaths.fr\/index.php\/wp-json\/wp\/v2\/comments?post=3376"}],"version-history":[{"count":7,"href":"https:\/\/jhmaths.fr\/index.php\/wp-json\/wp\/v2\/pages\/3376\/revisions"}],"predecessor-version":[{"id":3380,"href":"https:\/\/jhmaths.fr\/index.php\/wp-json\/wp\/v2\/pages\/3376\/revisions\/3380"}],"up":[{"embeddable":true,"href":"https:\/\/jhmaths.fr\/index.php\/wp-json\/wp\/v2\/pages\/3063"}],"wp:attachment":[{"href":"https:\/\/jhmaths.fr\/index.php\/wp-json\/wp\/v2\/media?parent=3376"}],"wp:term":[{"taxonomy":"folder","embeddable":true,"href":"https:\/\/jhmaths.fr\/index.php\/wp-json\/wp\/v2\/folder?post=3376"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}