Logarithm to base x of a constant

**Zyzz** · March 30th 2011, 03:36 AM

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

For example logx5 ?

**Plato** · March 30th 2011, 03:40 AM

Originally Posted by Zyzz

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

For example logx5 ?

$y=\log_x(5)=\dfrac{\ln(5)}{\ln(x)}$

**Prove It** · March 30th 2011, 03:41 AM

If you didn't know the change of base rule...

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

$\displaystyle x^y = 5$

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

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

$\displaystyle y = \frac{\ln{(5)}}{\ln{(x)}}$ .

**Zyzz** · March 30th 2011, 03:42 AM

nice. okay i didnt thank about that.

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