# How do you solve 5^x+1=625?

Oct 21, 2015

I found $x = 3.999$

#### Explanation:

Write it as:
${5}^{x} = 625 - 1$
${5}^{x} = 624$
taking the log in base $5$ on both sides:
$x = {\log}_{5} \left(624\right)$
To find $x$ we can try changing base and use a pocket calculator that can give us, say, the decimal log, as:
$x = {\log}_{5} \left(624\right) = \frac{{\log}_{10} \left(624\right)}{{\log}_{10} \left(5\right)} = 3.999$