(b) log10(0.01) = x<\/p>\n\n\n\n
x=<\/p>\n\n\n\n
The correct answer and explanation is :<\/strong><\/mark><\/p>\n\n\n\n We need to determine the value of ( x ) in the equation:<\/p>\n\n\n\n [ First, recall the definition of a logarithm:<\/p>\n\n\n\n [ In this case, ( b = 10 ), ( A = 0.01 ), and we need to find ( x ) such that:<\/p>\n\n\n\n [ Now, express ( 0.01 ) as a power of 10:<\/p>\n\n\n\n [ Thus, we can rewrite the equation as:<\/p>\n\n\n\n [ Since the bases are the same, we equate the exponents:<\/p>\n\n\n\n [ [ Logarithms are mathematical tools used to express exponents. The logarithmic function ( \\log_b(A) = C ) is the inverse of an exponential function and tells us what exponent ( C ) we need to raise ( b ) to in order to get ( A ).<\/p>\n\n\n\n In this problem, we are given the base-10 logarithm of 0.01 and asked to determine its value. The logarithm of a number less than 1 is always negative because raising 10 to a positive exponent always results in a number greater than 1.<\/p>\n\n\n\n To solve ( \\log_{10}(0.01) ), we rewrite 0.01 as a power of 10:<\/p>\n\n\n\n [ Using the logarithm rule:<\/p>\n\n\n\n [ we substitute ( 10^{-2} ) in place of ( 0.01 ):<\/p>\n\n\n\n [ This means that ( 10^{-2} = 0.01 ), confirming our result.<\/p>\n\n\n\n The logarithm of a number less than 1 is negative because the exponent needed to produce a fraction (like 0.01) is negative. This happens because dividing by 10 moves the decimal point to the left, making the number smaller.<\/p>\n\n\n\n Thus, the final answer is ( x = -2 ).<\/p>\n","protected":false},"excerpt":{"rendered":" (b) log10(0.01) = x x= The correct answer and explanation is : Solution: We need to determine the value of ( x ) in the equation: [\\log_{10}(0.01) = x] First, recall the definition of a logarithm: [\\log_b(A) = C \\quad \\text{means} \\quad b^C = A] In this case, ( b = 10 ), ( A […]<\/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-199013","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/199013","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=199013"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/199013\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=199013"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=199013"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=199013"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Solution:<\/h3>\n\n\n\n
\\log_{10}(0.01) = x
]<\/p>\n\n\n\n
\\log_b(A) = C \\quad \\text{means} \\quad b^C = A
]<\/p>\n\n\n\n
10^x = 0.01
]<\/p>\n\n\n\n
0.01 = 10^{-2}
]<\/p>\n\n\n\n
10^x = 10^{-2}
]<\/p>\n\n\n\n
x = -2
]<\/p>\n\n\n\nFinal Answer:<\/h3>\n\n\n\n
\\log_{10}(0.01) = -2
]<\/p>\n\n\n\n
\n\n\n\nExplanation (300 Words):<\/h3>\n\n\n\n
0.01 = 1\/100 = 10^{-2}
]<\/p>\n\n\n\n
\\log_{10}(10^C) = C
]<\/p>\n\n\n\n
\\log_{10}(10^{-2}) = -2
]<\/p>\n\n\n\nWhy is the Answer Negative?<\/h3>\n\n\n\n