# How do you solve 12^r=13?

Nov 25, 2016

#### Explanation:

You can use either the natural logarithm or the base 10 logarithm for this step. (I will use the base 10):

${\log}_{10} \left({12}^{r}\right) = {\log}_{10} \left(13\right)$

Use the property of all logarithms $\log \left({a}^{b}\right) = \left(b\right) \log \left(a\right)$:

$\left(r\right) {\log}_{10} \left(12\right) = {\log}_{10} \left(13\right)$

Divide both sides by ${\log}_{10} \left(12\right)$:

$r = {\log}_{10} \frac{13}{\log} _ 10 \left(12\right)$

$r \approx 1.032$