{"id":6013,"date":"2021-10-04T22:22:56","date_gmt":"2021-10-04T16:52:56","guid":{"rendered":"https:\/\/mathemerize.com\/?p=6013"},"modified":"2021-10-04T22:25:36","modified_gmt":"2021-10-04T16:55:36","slug":"logarithm-examples","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/logarithm-examples\/","title":{"rendered":"Logarithm Examples"},"content":{"rendered":"

Here you will learn some logarithm examples for better understanding of logarithm concepts<\/a><\/span>.<\/p>\n\n\n

\n
\n\n \n

Example 1 : <\/span> If \\(log_e x\\) – \\(log_e y\\) = a, \\(log_e y\\) – \\(log_e z\\) = b & \\(log_e z\\) – \\(log_e x\\) = c, then find the value of \\(({x\\over y})^{b-c}\\) \\(\\times\\)\n \\(({y\\over z})^{c-a}\\) \\(\\times\\) \\(({z\\over x})^{a-b}\\). <\/p>\n

Solution : <\/span>\\(log_e x\\) – \\(log_e y\\) = a \\(\\implies\\) \\(log_e {x\\over y}\\) = a \\(\\implies\\) \\(x\\over y\\) = \\(e^a\\)

\\(log_e y\\) – \\(log_e z\\) = b \\(\\implies\\) \\(log_e {y\\over z}\\) = b \\(\\implies\\) \\(y\\over z\\) = \\(e^b\\)

\\(log_e z\\) – \\(log_e x\\) = c \\(\\implies\\) \\(log_e {z\\over x}\\) = c \\(\\implies\\) \\(z\\over x\\) = \\(e^c\\)

\\(\\therefore\\)     \\((e^a)^{b-c}\\) \\(\\times\\) \\((e^b)^{c-a}\\) \\(\\times\\) \\((e^c)^{a-b}\\)

=     \\(e^{a(b-c)+b(c-a)+c(a-b)}\\) = \\(e^0\\) = 1<\/p>\n


\n\n \n

Example 2 : <\/span> If \\(log_a x\\) = p and \\(log_b {x^2}\\) = q then \\(log_x \\sqrt{ab}\\) is equal to- <\/p>\n

Solution : <\/span>\\(log_a x\\) = p \\(\\implies\\) \\(a^p\\) = x \\(\\implies\\) a = \\(x^{1\/p}\\)

Similarly     \\(b^q\\) = \\(x^2\\) \\(\\implies\\) b = \\(x^{2\/q}\\)

\n Now,     \\(log_x \\sqrt{ab}\\) = \\(log_x \\sqrt{x^{1\/p}x^{2\/q}}\\) = \\(log_x x^{({1\\over p}+{2\\over q}){1\\over 2}}\\) = \\(1\\over {2p}\\) + \\(1\\over q\\).\n <\/p>


\n\n \n

Example 3 : <\/span>Solve for x : \\(2^{x+2}\\) > \\(({1\\over 4})^{1\/x}\\)<\/p>\n

Solution : <\/span> We have \\(2^{x+2}\\) > \\(2^{-2\/x}\\).

Since the base 2 > 1, we have x + 2 > \\(-2\\over x\\)

(the sign of inequality is retained)

Now     x + 2 + \\(-2\\over x\\) > 0 \\(\\implies\\) \\({x^2 + 2x + 2}\\over x\\) > 0

\\(\\implies\\)     \\(({x+1})^2 + 1\\over x\\) > 0

\\(\\implies\\)     x \\(\\in\\) (0,\\(\\infty\\)).<\/p>\n
\n

Practice these given logarithm examples to test your knowledge on concepts of logarithm.<\/p>\n <\/div>\n <\/div>\n","protected":false},"excerpt":{"rendered":"

Here you will learn some logarithm examples for better understanding of logarithm concepts. Example 1 : If \\(log_e x\\) – \\(log_e y\\) = a, \\(log_e y\\) – \\(log_e z\\) = b & \\(log_e z\\) – \\(log_e x\\) = c, then find the value of \\(({x\\over y})^{b-c}\\) \\(\\times\\) \\(({y\\over z})^{c-a}\\) \\(\\times\\) \\(({z\\over x})^{a-b}\\). Solution : \\(log_e …<\/p>\n

Logarithm Examples<\/span> Read More »<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"default","ast-global-header-display":"","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":"","theme-transparent-header-meta":"default","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":""},"categories":[13],"tags":[],"yoast_head":"\nLogarithm Examples - Mathemerize<\/title>\n<meta name=\"description\" content=\"Solve these Logarithm examples to practice and test your knowledge of Logarithm concepts.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mathemerize.com\/logarithm-examples\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Logarithm Examples - 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