# Thread: Logarithm to base x of a constant

1. ## 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 ?

2. 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 log
x5 ?
$\displaystyle y=\log_x(5)=\dfrac{\ln(5)}{\ln(x)}$

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

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

$\displaystyle \displaystyle x^y = 5$

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

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

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

4. nice. okay i didnt thank about that.