{"id":7200,"date":"2021-10-23T01:04:19","date_gmt":"2021-10-22T19:34:19","guid":{"rendered":"https:\/\/mathemerize.com\/?p=7200"},"modified":"2021-10-25T00:48:57","modified_gmt":"2021-10-24T19:18:57","slug":"solve-for-x-2x-2-1over-41over-x","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/solve-for-x-2x-2-1over-41over-x\/","title":{"rendered":"Solve for x : \\(2^{x + 2}\\) > \\(({1\\over 4})^{1\\over 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 the inequality is retained)<\/p>\n

Now x + 2 + \\(2\\over x\\)\u00a0 \\(\\implies\\) \\(x^2 + 2x + 2\\over x\\) > 0<\/p>\n

\\(\\implies\\) \\((x + 1)^2 + 1\\over x\\) > 0\u00a0 \\(\\implies\\)\u00a0 x \\(\\in\\) \\((0, \\infty)\\)<\/p>\n

\n

Similar Questions<\/h3>\n

Find the value of \\(2log{2\\over 5}\\) + \\(3log{25\\over 8}\\) \u2013 \\(log{625\\over 128}\\).<\/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

If \\(log_e x\\) \u2013 \\(log_e y\\) = a, \\(log_e y\\) \u2013 \\(log_e z\\) = b & \\(log_e z\\) \u2013 \\(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}\\).<\/a><\/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 the inequality is retained) Now x + 2 + \\(2\\over x\\)\u00a0 \\(\\implies\\) \\(x^2 + 2x + 2\\over x\\) > 0 \\(\\implies\\) \\((x + 1)^2 + 1\\over x\\) > 0\u00a0 …<\/p>\n

Solve for x : \\(2^{x + 2}\\) > \\(({1\\over 4})^{1\\over 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":[55,43],"tags":[],"yoast_head":"\nSolve for x : \\(2^{x + 2}\\) > \\(({1\\over 4})^{1\\over x}\\).<\/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-2x-2-1over-41over-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\\over x}\\).\" \/>\n<meta property=\"og:description\" content=\"Solution : We have (2^{x + 2}) > (2^{2\/x}). Since the base 2 > 1, we have x + 2 > -(2over x) (the sign of the inequality is retained) Now x + 2 + (2over x)\u00a0 (implies) (x^2 + 2x + 2over x) > 0 (implies) ((x + 1)^2 + 1over x) > 0\u00a0 … Solve for x : (2^{x + 2}) > (({1over 4})^{1over x}). 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