{"id":6791,"date":"2021-10-21T17:09:16","date_gmt":"2021-10-21T11:39:16","guid":{"rendered":"https:\/\/mathemerize.com\/?p=6791"},"modified":"2021-10-24T23:54:28","modified_gmt":"2021-10-24T18:24:28","slug":"find-the-range-of-the-function-log_sqrt22-log_216sin2x1","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/find-the-range-of-the-function-log_sqrt22-log_216sin2x1\/","title":{"rendered":"Find the range of the function \\(log_{\\sqrt{2}}(2-log_2(16sin^2x+1))\\)"},"content":{"rendered":"

Solution :<\/h2>\n

Now 1 \\(\\le\\) \\(16sin^2x\\) + 1) \\(\\le\\) 17<\/p>\n

0 \\(\\le\\) \\(log_2(16sin^2x+1)\\) \\(\\le\\) \\(log_217\\)<\/p>\n

2 – \\(log_217\\) \\(\\le\\) 2 – \\(log_2(16sin^2x+1)\\) \\(\\le\\) 2<\/p>\n

Now consider 0 < 2 – \\(log_2(16sin^2x+1)\\) \\(\\le\\) 2<\/p>\n

-\\(\\infty\\) < \\(log_{\\sqrt{2}}(2-log_2(16sin^2x+1))\\) \\(\\le\\) \\(log_{\\sqrt{2}}2\\) = 2<\/p>\n

the range is (-\\(\\infty\\), 2]<\/p>\n

\n

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Solution : Now 1 \\(\\le\\) \\(16sin^2x\\) + 1) \\(\\le\\) 17 0 \\(\\le\\) \\(log_2(16sin^2x+1)\\) \\(\\le\\) \\(log_217\\) 2 – \\(log_217\\) \\(\\le\\) 2 – \\(log_2(16sin^2x+1)\\) \\(\\le\\) 2 Now consider 0 < 2 – \\(log_2(16sin^2x+1)\\) \\(\\le\\) 2 -\\(\\infty\\) < \\(log_{\\sqrt{2}}(2-log_2(16sin^2x+1))\\) \\(\\le\\) \\(log_{\\sqrt{2}}2\\) = 2 the range is (-\\(\\infty\\), 2] Similar Questions If y = 2[x] + 3 & y …<\/p>\n

Find the range of the function \\(log_{\\sqrt{2}}(2-log_2(16sin^2x+1))\\)<\/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":[50,43],"tags":[],"yoast_head":"\nFind the range of the function \\(log_{\\sqrt{2}}(2-log_2(16sin^2x+1))\\)<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" 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