# How do you solve 0.73^x=0.25?

Oct 29, 2016

$x = 4.405$

#### Explanation:

$0.25$ is most certainly not one of the powers of $0.73$

The fact that the variable is in the index is an indication that you need to use logs.

$\log {0.73}^{x} = \log 0.25 \text{ } \leftarrow$ log both sides

$x \log 0.73 = \log 0.25 \text{ } \leftarrow$ power rule

$x = \log \frac{0.25}{\log} 0.73 \text{ } \leftarrow$ isolate $x$

$x = 4.405 \text{ } \leftarrow$ use a calculator to get the value of $x$