range of ln x 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 Have a nice day from the Philippines Answer link
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 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
range of ln x
range of ln x
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F x ln x 4 Domain Range Graph And Its Inverse YouTube
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Math12 Chapter 8 Exponential And Its Inverse Lnx Function
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The natural logarithm of x is the power to which e would have to be raised to equal x For example ln 7 5 is 2 0149 because e2 0149 7 5 The natural logarithm of e itself ln e is 1 because e1 e while the natural logarithm of 1 is 0 since e0 1 A logarithmic function involves logarithms Its basic form is f x log x or ln x Learn about the conversion of an exponential function to a logarithmic function know about natural and common logarithms and check the properties of logarithms
Wolfram Alpha is a great tool for finding the domain and range of a function It also shows plots of the function and illustrates the domain and range on a number line to enhance your mathematical intuition The domain of ln x is x 0 which means that x can only accept positive real values The natural logarithm represented by ln x is the logarithm having the base e This complete guide will teach you
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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 Actually the range of y ln x the possible output values y of your function is all the real y You can see this from the graph as well graph ln x 5 55 5 55 2 774 2 775
Properties of ln x The domain is the set of all positive real numbers x 0 The range is the set of all real numbers 1 y 1 Algebraic properties If a and b are any positive real numbers and r is any real number then ln 1 0 ln ab ln a ln b Product rule ln a ln a ln b Quotient b rule ln ar r ln a Power rule ln 1 ln What about the range Since the output of ln is all of R the collection of inputs being fed to sine is all real numbers And we know that the collection of outputs for that collection of inputs is 1 1 So I bet that the output of sin ln x the range is 1 1
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range of ln x - Wolfram Alpha is a great tool for finding the domain and range of a function It also shows plots of the function and illustrates the domain and range on a number line to enhance your mathematical intuition