# How do you solve 2^(x-9) = 5 ?

##### 1 Answer
Aug 12, 2016

$x = 11.3223$

#### Explanation:

As ${2}^{x - 9} = 5$, writing in logarithmic form we have

$\left(x - 9\right) = {\log}_{2} \left(5\right)$, which can be also written as

$\left(x - 9\right) = \log \frac{5}{\log} 2$

= $\frac{0.6990}{0.3010} = 2.3223$

and $x = 9 + 2.3223 = 11.3223$