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Math Help - Logarithm to base x of a constant

  1. #1
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    Logarithm to base x of a constant

    How would u differentiate the logarithm in which the base is the variable and the other number is a constant?

    For example log
    x5 ?
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  2. #2
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    Quote Originally Posted by Zyzz View Post
    How would u differentiate the logarithm in which the base is the variable and the other number is a constant?

    For example log
    x5 ?
    y=\log_x(5)=\dfrac{\ln(5)}{\ln(x)}
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  3. #3
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    If you didn't know the change of base rule...

    \displaystyle y = \log_{x}{(5)}

    \displaystyle x^y = 5

    \displaystyle \ln{\left(x^y\right)} = \ln{(5)}

    \displaystyle y\ln{(x)} = \ln{(5)}

    \displaystyle y = \frac{\ln{(5)}}{\ln{(x)}}.
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  4. #4
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    nice. okay i didnt thank about that.
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