Question

How do you solve `13^v=76`?

Answer 1

`v=log_13 76 ~~1.6884`

Explanation:

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

Answer 2

I found: `v=1.68843`

Explanation:

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