# How do you solve 3^(2x+1) = 5?

Aug 3, 2017

$x = 0.232$ (to 3 sf)

#### Explanation:

We will not attempt to treat this as an exponential equation by working with the bases, because $5$ is not a power of $3$.

Find the log of both sides.

$\log {3}^{2 x + 1} = \log 5 \text{ } \leftarrow$ use the log power law

$\left(2 x + 1\right) \log 3 = \log 5 \text{ } \leftarrow$ isolate the $x$ term

$2 x + 1 = \log \frac{5}{\log} 3$

$2 x = \log \frac{5}{\log} 3 - 1$

$x = \left(\log \frac{5}{\log} 3 - 1\right) \div 2$

There are no laws to simplify this, so use a calculator to find a value for $x$

$x = 0.23248676$