{"id":6838,"date":"2021-10-21T19:40:05","date_gmt":"2021-10-21T14:10:05","guid":{"rendered":"https:\/\/mathemerize.com\/?p=6838"},"modified":"2021-10-22T17:04:36","modified_gmt":"2021-10-22T11:34:36","slug":"solve-for-x-2x2-1over-41-x","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/solve-for-x-2x2-1over-41-x\/","title":{"rendered":"Solve for x : \\(2^{x+2}\\) > \\(({1\\over 4})^{1\/x}\\)"},"content":{"rendered":"

Solution :<\/h2>\n

We have \\(2^{x+2}\\) > \\(2^{-2\/x}\\)<\/p>\n

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

(the sign of inequality is retained)<\/p>\n

Now, x + 2 + \\(-2\\over x\\) > 0 \\(\\implies\\) \\({x^2 + 2x + 2}\\over x\\) > 0<\/p>\n

\\(\\implies\\)  \\(({x+1})^2 + 1\\over x\\) > 0<\/p>\n

\\(\\implies\\)  x \\(\\in\\) (0,\\(\\infty\\)).<\/p>\n","protected":false},"excerpt":{"rendered":"

Solution : 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\\) …<\/p>\n

Solve for x : \\(2^{x+2}\\) > \\(({1\\over 4})^{1\/x}\\)<\/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":[43],"tags":[],"yoast_head":"\nSolve for x : \\(2^{x+2}\\) > \\(({1\\over 4})^{1\/x}\\) - Mathemerize<\/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\/solve-for-x-2x2-1over-41-x\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Solve for x : \\(2^{x+2}\\) > \\(({1\\over 4})^{1\/x}\\) - 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