# How do you solve 13^v=76?

Aug 24, 2016

$v = {\log}_{13} 76 \approx 1.6884$

#### Explanation:

You probably need to use a calculator or spreadsheet to evaluate the base 13 log.

Aug 24, 2016

I found: $v = 1.68843$

#### Explanation:

I would try using logarithms.
Take the log in base $13$ on both sides:
${\log}_{13} \left({13}^{v}\right) = {\log}_{13} \left(76\right)$
On the left we can write:
$v {\log}_{13} \left(13\right) = {\log}_{13} \left(76\right)$
with: ${\log}_{13} \left(13\right) = 1$
so:
$v = {\log}_{13} \left(76\right)$
now we seem stuck but if we have a calculator we can change base and evaluate it:
$v = \frac{\ln \left(76\right)}{\ln \left(13\right)} = 1.68843$