{"id":9759,"date":"2022-01-26T23:37:09","date_gmt":"2022-01-26T18:07:09","guid":{"rendered":"https:\/\/mathemerize.com\/?p=9759"},"modified":"2022-01-26T23:38:32","modified_gmt":"2022-01-26T18:08:32","slug":"logarithmic-function","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/logarithmic-function\/","title":{"rendered":"Logarithmic Function – Graph, Definition, Domain and Range"},"content":{"rendered":"

Here you will learn what is logarithmic function graph, formula, domain and range.<\/p>\n

Let’s begin –<\/p>\n

Logarithmic Function<\/h2>\n

Definition<\/strong> : If a > 0 and a \\(\\ne\\) 1, then the function defined by f(x) = \\(log_a x\\), x > 0 is called the logarithmic function.<\/p>\n

We know that logarithmic function and the exponential function are inverse of each other.<\/p>\n

i.e\u00a0 \u00a0 \\(log_a x\\) = y\u00a0 \\(\\iff\\)\u00a0 x = \\(a^y\\)<\/p><\/blockquote>\n

Also Read<\/strong> : Types of Functions in Maths \u2013 Domain and Range<\/a><\/p>\n

Logarithmic Function Graph<\/h2>\n

Case 1<\/strong> : When a > 1,<\/p>\n

In this case, we have<\/p>\n

y = \\(log_a x\\) = \\(\\begin{cases} < 0, & \\text{for}\\ 0 < x < 1 \\\\ = 0, & \\text{for}\\ x = 1 \\\\ > 0, & \\text{for}\\ x > 1 \\end{cases}\\).<\/p>\n

Also, the value of y increase with increase in x.<\/p>\n

Thus, the graph f(x) = \\(log_a x\\) for a > 1 is\u00a0 :<\/p>\n

\"logarithmic<\/p>\n

Case 2<\/strong> : When 0 < a < 1<\/p>\n

In this case, we have<\/p>\n

y = \\(log_a x\\) = \\(\\begin{cases} > 0, & \\text{for}\\ 0 < x < 1 \\\\ = 0, & \\text{for}\\ x = 1 \\\\ < 0, & \\text{for}\\ x > 1 \\end{cases}\\).<\/p>\n

Also, the value of y decrease with the increase in x.<\/p>\n

Thus, the graph y = \\(log_a x\\) for 0 < a <1 is\u00a0 :<\/p>\n

\"logarithmic<\/p>\n

Domain and Range<\/h2>\n

We observe that the domain of the logarithmic function is the set of all non-negative real numbers i.e. \\((0, \\infty)\\) and the range is the set R of all real numbers.<\/p>\n

Domain<\/strong> : \\((0, \\infty)\\)<\/p>\n

Range<\/strong> : R<\/p><\/blockquote>\n","protected":false},"excerpt":{"rendered":"

Here you will learn what is logarithmic function graph, formula, domain and range. Let’s begin – Logarithmic Function Definition : If a > 0 and a \\(\\ne\\) 1, then the function defined by f(x) = \\(log_a x\\), x > 0 is called the logarithmic function. We know that logarithmic function and the exponential function are …<\/p>\n

Logarithmic Function – Graph, Definition, Domain and Range<\/span> Read More »<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","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":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":""},"categories":[26],"tags":[810,811],"yoast_head":"\nLogarithmic Function - Graph, Definition, Domain and Range<\/title>\n<meta name=\"description\" content=\"In this post you will learn what is logarithmic function graph and definition, domain and range of exponential function.\" \/>\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\/logarithmic-function\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Logarithmic Function - 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