{"id":6834,"date":"2021-10-21T19:35:53","date_gmt":"2021-10-21T14:05:53","guid":{"rendered":"https:\/\/mathemerize.com\/?p=6834"},"modified":"2021-10-25T00:48:50","modified_gmt":"2021-10-24T19:18:50","slug":"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-xover-yb-c-times-yover-zc-a","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/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-xover-yb-c-times-yover-zc-a\/","title":{"rendered":"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}\\)."},"content":{"rendered":"

Solution :<\/h2>\n

\\(log_e x\\) – \\(log_e y\\) = a \\(\\implies\\) \\(log_e {x\\over y}\\) = a \\(\\implies\\) \\(x\\over y\\) = \\(e^a\\)<\/p>\n

\\(log_e y\\) – \\(log_e z\\) = b \\(\\implies\\) \\(log_e {y\\over z}\\) = b \\(\\implies\\) \\(y\\over z\\) = \\(e^b\\)<\/p>\n

\\(log_e z\\) – \\(log_e x\\) = c \\(\\implies\\) \\(log_e {z\\over x}\\) = c \\(\\implies\\) \\(z\\over x\\) = \\(e^c\\)<\/p>\n

\\(\\therefore\\)\u00a0 \\((e^a)^{b-c}\\) \\(\\times\\) \\((e^b)^{c-a}\\) \\(\\times\\) \\((e^c)^{a-b}\\)<\/p>\n

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

\n

Similar Questions<\/h3>\n

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

Evaluate the given log : \\(81^{l\\over {log_5 3}}\\) + \\(27^{log_9 36}\\) + \\(3^{4\\over {log_7 9}}\\).<\/a><\/p>\n

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

Find the value of \\(2log{2\\over 5}\\) + \\(3log{25\\over 8}\\) \u2013 \\(log{625\\over 128}\\).<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

Solution : \\(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\\) = …<\/p>\n

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}\\).<\/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":[55,43],"tags":[],"yoast_head":"\nIf \\(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}\\).<\/title>\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\/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-xover-yb-c-times-yover-zc-a\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"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}\\).\" \/>\n<meta property=\"og:description\" content=\"Solution : (log_e x) – (log_e y) = a (implies) (log_e {xover y}) = a (implies) (xover y) = (e^a) (log_e y) – (log_e z) = b (implies) (log_e {yover z}) = b (implies) (yover z) = (e^b) (log_e z) – (log_e x) = c (implies) (log_e {zover x}) = c (implies) (zover x) = … 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 (({xover y})^{b-c}) (times) (({yover z})^{c-a}) (times) (({zover x})^{a-b}). 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