# How to substitute log_(10) for ln function?

How to substitute ${\mathrm{log}}_{10}$ for $\mathrm{ln}$ function?
Im wondering how I could go about substituting ${\mathrm{log}}_{10}$ for $\mathrm{ln}$ in the following formula?
$y=a+b\mathrm{ln}\left(x+c\right)$
Is there a simple way of doing this?
Cheers
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Keegan Barry
Hint:
For any $\phantom{\rule{thickmathspace}{0ex}}1\ne a,b>0\phantom{\rule{thickmathspace}{0ex}}$
${\mathrm{log}}_{a}x=\frac{{\mathrm{log}}_{b}x}{{\mathrm{log}}_{b}a}$

auto23652im
There is a a formula to change from base $k$ to base $b$. See ${\mathrm{log}}_{b}x=\frac{{\mathrm{log}}_{k}x}{{\mathrm{log}}_{k}b}.$
In your equation you have $\mathrm{log}\left(x+c\right)$ ($\mathrm{log}$ is the natural logarithm). If we apply the change of base rule we get:
$\mathrm{log}\left(x+c\right)=\frac{{\mathrm{log}}_{10}\left(x+c\right)}{{\mathrm{log}}_{10}e},$
where $e=\mathrm{exp}\left(1\right)$ is the exponetial of $1$$e=2.71828$
$y=a+\frac{b}{{\mathrm{log}}_{10}e}{\mathrm{log}}_{10}\left(x+c\right),$