{"id":4814,"date":"2023-07-14T10:54:26","date_gmt":"2023-07-14T17:54:26","guid":{"rendered":"https:\/\/mathtalk.sdsu.edu\/wordpress\/?page_id=4814"},"modified":"2023-08-11T09:48:33","modified_gmt":"2023-08-11T16:48:33","slug":"logarithms-lesson-6","status":"publish","type":"page","link":"https:\/\/mathtalk.sdsu.edu\/wordpress\/mathtalk-for-students\/logarithms-unit\/logarithms-lesson-6\/","title":{"rendered":"Logarithms Lesson 6"},"content":{"rendered":"\n<h3 class=\"wp-block-heading\"><strong><strong>Justifying the Product Rule for Logarithmic Expressions<\/strong><\/strong><\/h3>\n\n\n\n<p>Josh and Arobindo write two equivalent exponential expressions that represent the time it takes for the amount of mold to increase by one factor, and then by another. In doing so, they justify a rule for rewriting logarithmic expressions of a certain form.<\/p>\n\n\n\n<h5 class=\"wp-block-heading\"><strong><a href=\"https:\/\/mathtalk.sdsu.edu\/wordpress\/mathtalk-for-students\/logarithms-unit\/logarithms-lesson-6\/logarithms-lesson-6-episode-1\/\" data-type=\"page\" data-id=\"4964\">Episode 1: Making Sense<\/a><\/strong><\/h5>\n\n\n\n<p>The students model on their number line the mold growth on the pizza over two consecutive time periods. They then calculate the total elapsed time over the two periods of time.&nbsp;&nbsp;<\/p>\n\n\n\n<h5 class=\"wp-block-heading\"><strong><a href=\"https:\/\/mathtalk.sdsu.edu\/wordpress\/mathtalk-for-students\/logarithms-unit\/logarithms-lesson-6\/logarithms-lesson-6-episode-2\/\" data-type=\"page\" data-id=\"4959\">Episode 2: Exploring<\/a><\/strong><\/h5>\n\n\n\n<p>Josh and Arobindo consider another student\u2019s equation that is meant to describe the mold growth over two consecutive time periods. They decide the student has written an incorrect equation and propose a new equation. They explain why the two logarithmic expressions in their equation are equivalent.<\/p>\n\n\n\n<h5 class=\"wp-block-heading\"><strong><a href=\"https:\/\/mathtalk.sdsu.edu\/wordpress\/mathtalk-for-students\/logarithms-unit\/logarithms-lesson-6\/logarithms-lesson-6-episode-3\/\" data-type=\"page\" data-id=\"4967\">Episode 3: Repeating Your Reasoning<\/a><\/strong><\/h5>\n\n\n\n<p>Arobindo and Josh fill in the blanks of the equation log<sub>3<\/sub>&nbsp;(___) + log<sub>3<\/sub>&nbsp;(___) = log<sub>3<\/sub>&nbsp;(1,000) to make the equation true. They justify their answer.<\/p>\n\n\n\n<h5 class=\"wp-block-heading\"><strong><a href=\"https:\/\/mathtalk.sdsu.edu\/wordpress\/mathtalk-for-students\/logarithms-unit\/logarithms-lesson-6\/logarithms-lesson-6-episode-4\/\" data-type=\"page\" data-id=\"4971\">Episode 4: Reflecting<\/a>&nbsp;<\/strong><\/h5>\n\n\n\n<p>The students find a logarithmic expression that is equivalent to log<sub>3<\/sub>&nbsp;(x) + log<sub>3<\/sub>&nbsp;(y). They explain what their equation means in terms of the moldy food context and justify their proposed relationship using a number line.<\/p>\n\n\n\n<div class=\"wp-block-buttons is-layout-flex wp-block-buttons-is-layout-flex\">\n<div class=\"wp-block-button\"><a class=\"wp-block-button__link has-background wp-element-button\" href=\"https:\/\/mathtalk.sdsu.edu\/wordpress\/\" style=\"background-color:#2d4059\">Home<\/a><\/div>\n\n\n\n<div class=\"wp-block-button\"><a class=\"wp-block-button__link has-background wp-element-button\" href=\"https:\/\/mathtalk.sdsu.edu\/wordpress\/mathtalk-for-students\/\" style=\"background-color:#2d4059\">Units<\/a><\/div>\n\n\n\n<div class=\"wp-block-button\"><a class=\"wp-block-button__link has-background wp-element-button\" href=\"https:\/\/mathtalk.sdsu.edu\/wordpress\/mathtalk-for-students\/logarithms-unit\/\" style=\"background-color:#2d4059\">Logarithms<\/a><\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Justifying the Product Rule for Logarithmic Expressions Josh and Arobindo write two equivalent exponential expressions that represent the time it takes for the amount of mold to increase by one factor, and then by another. In doing so, they justify a rule for rewriting logarithmic expressions of a certain form. Episode 1: Making Sense The [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"parent":141,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-4814","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/4814","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/comments?post=4814"}],"version-history":[{"count":7,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/4814\/revisions"}],"predecessor-version":[{"id":5146,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/4814\/revisions\/5146"}],"up":[{"embeddable":true,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/141"}],"wp:attachment":[{"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/media?parent=4814"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}