{"id":170634,"date":"2024-11-19T21:57:53","date_gmt":"2024-11-19T21:57:53","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=170634"},"modified":"2024-11-19T21:57:54","modified_gmt":"2024-11-19T21:57:54","slug":"the-magnitude-m-of-an-earthquake-is-defined-to-be-m-log-startfraction-i-over-s-endfraction","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/11\/19\/the-magnitude-m-of-an-earthquake-is-defined-to-be-m-log-startfraction-i-over-s-endfraction\/","title":{"rendered":"The magnitude, m, of an earthquake is defined to be m = log startfraction i over s endfraction"},"content":{"rendered":"\n<p>The magnitude, m, of an earthquake is defined to be m = log startfraction i over s endfraction, where i is the intensity of the earthquake (measured by the amplitude of the seismograph wave) and s is the intensity of a &#8220;standard&#8221; earthquake, which is barely detectable. what is the magnitude of an earthquake that is 35 times more intense than a standard earthquake? use a calculator. round your answer to the nearest tenth. \u20131.5 \u20130.5 1.5 3.6<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>To solve this problem, we need to use the given formula for the magnitude ( m ) of an earthquake:<\/p>\n\n\n\n<p>[<br>m = \\log \\left( \\frac{i}{s} \\right)<br>]<\/p>\n\n\n\n<p>Where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>( m ) is the magnitude of the earthquake.<\/li>\n\n\n\n<li>( i ) is the intensity of the earthquake (measured by the amplitude of the seismograph wave).<\/li>\n\n\n\n<li>( s ) is the intensity of a &#8220;standard&#8221; earthquake, which is barely detectable.<\/li>\n<\/ul>\n\n\n\n<p>The problem states that the earthquake is 35 times more intense than the standard earthquake, so we can express this as:<\/p>\n\n\n\n<p>[<br>i = 35s<br>]<\/p>\n\n\n\n<p>Substitute this into the formula for ( m ):<\/p>\n\n\n\n<p>[<br>m = \\log \\left( \\frac{35s}{s} \\right)<br>]<\/p>\n\n\n\n<p>Simplifying the fraction:<\/p>\n\n\n\n<p>[<br>m = \\log (35)<br>]<\/p>\n\n\n\n<p>Next, we need to calculate the logarithm of 35. Using a calculator:<\/p>\n\n\n\n<p>[<br>\\log (35) \\approx 1.544<br>]<\/p>\n\n\n\n<p>Rounding this value to the nearest tenth:<\/p>\n\n\n\n<p>[<br>m \\approx 1.5<br>]<\/p>\n\n\n\n<p>Therefore, the magnitude of the earthquake is <strong>1.5<\/strong>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation:<\/h3>\n\n\n\n<p>The formula ( m = \\log \\left( \\frac{i}{s} \\right) ) is based on a logarithmic scale. The logarithmic scale is used to represent large variations in the intensity of earthquakes in a more manageable form. In this case, we are comparing the intensity of the earthquake to that of a standard earthquake, which has a very small intensity value (( s )).<\/p>\n\n\n\n<p>The problem tells us that the earthquake is 35 times more intense than the standard earthquake. This means that the ratio of ( i ) (the intensity of the earthquake) to ( s ) (the standard intensity) is 35. Taking the logarithm of this ratio gives us the magnitude of the earthquake. Since logarithms are a powerful way to deal with large differences in numbers, they allow us to express the magnitude of earthquakes in a compact and manageable way.<\/p>\n\n\n\n<p>The final answer of 1.5 indicates that the earthquake is significantly stronger than the barely detectable standard earthquake.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The magnitude, m, of an earthquake is defined to be m = log startfraction i over s endfraction, where i is the intensity of the earthquake (measured by the amplitude of the seismograph wave) and s is the intensity of a &#8220;standard&#8221; earthquake, which is barely detectable. what is the magnitude of an earthquake that [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-170634","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/170634","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=170634"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/170634\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=170634"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=170634"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=170634"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}