# How do you express log_3 10 in terms of common logs?

Dec 30, 2016

I changed base to base $10$:

#### Explanation:

You can change base, remembering that if you want to change base, say, from $b$ to $c$, you have:
${\log}_{b} \left(x\right) = \frac{{\log}_{c} \left(x\right)}{{\log}_{c} \left(b\right)}$
In your case we can write:
log_3(10)=(log_(10)(10))/(log_(10)(3)
Changing into base $10$.

Now you can evaluate the numerator by yourself....try it!