domain of ln x Domain and range ln x Compute answers using Wolfram s breakthrough technology knowledgebase relied on by millions of students professionals For math science nutrition history geography engineering mathematics linguistics sports finance music
Determine the domain and range Domain 0 x x 0 0 x x 0 Range y y R y y Free math problem solver answers your algebra geometry trigonometry calculus and statistics homework questions with step by step explanations just like a math tutor What is the domain and range of y ln x Algebra Expressions Equations and Functions Domain and Range of a Function 1 Answer Leland Adriano Alejandro Feb 8 2016 Domain x 0 Range x Explanation The graph of y lnx x can only be all positive and y can take positive or negative values graph y ln x 10 10 5 5
domain of ln x
domain of ln x
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Domain Of Ln x 2 y Set builder Form Picture Form And Inequality Form
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Mkkitech Lnx2y2 Domain
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In general the logarithmic function always has positive x and never crosses the y axis always intersects the x axis at x 1 in other words it passes through 1 0 equals 1 when x a in other words it passes through a 1 is an Injective one to one function Its Domain is the Positive Real Numbers 0 Domain 0 Range Explanation Let f x ln x f x is defined x 0 Hence the domain of f x is 0 Consider lim x 0 f x and lim x f x Hence the range of f x is We can visualise these results from the graph on lnx below
Identify the domain of a logarithmic function Before working with graphs we will take a look at the domain the set of input values for which the logarithmic function is defined Recall that the exponential function is defined as displaystyle y b x y bx for any real number x and constant displaystyle b 0 b 0 displaystyle b ne 1 The principal value of the natural logarithm is implemented in the Wolfram Language as Log x which is equivalent to Log E x This function is illustrated above in the complex plane
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X Also since the logarithmic and exponential functions switch the x and y values the domain and range of the exponential function are interchanged for the logarithmic function Therefore the domain of the logarithm function with base b is 0 b is 0 The domain of log function y log x is x 0 or 0 The range of any log function is the set of all real numbers R Example Find the domain and range of the logarithmic function f x 2 log 2x 4 5 Solution For finding domain set the argument of the function greater than 0 and solve for x 2x 4 0 2x 4 x 2 Thus
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domain of ln x - Domain 0 Range Explanation Let f x ln x f x is defined x 0 Hence the domain of f x is 0 Consider lim x 0 f x and lim x f x Hence the range of f x is We can visualise these results from the graph on lnx below