# How do you simplify  log10^9 + 10^log5?

Jul 21, 2016

I found $14$ (supposing base $10$ for the logs).

#### Explanation:

Supposing the base of the logs being $10$ we see that:

$\log {10}^{9} = 9$

and:

${10}^{\log 5} = 5$

both derive from the definition of log (specifically in base $10$):
${\log}_{10} x = a \to x = {10}^{a}$

So basically you expression becomes:
$\log {10}^{9} + {10}^{\log 5} = 9 + 5 = 14$

If the base is not $10$ then it depends...