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

Feb 27, 2016

$x \approx 0.73$

#### Explanation:

$1$. Notice that the powers on both sides of the equation do not have the same base. Thus, you must log both sides.

$\log \left({3}^{2 x}\right) = \log \left(5\right)$

$2$. Recall the log rule: ${\log}_{b} \left({m}^{\textcolor{red}{n}}\right) = \textcolor{red}{n} {\log}_{b} \left(m\right)$. Thus, in your equation, bring down the exponent, $2 x$.

$2 x \log \left(3\right) = \log \left(5\right)$

$3$. Solve for $x$.

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

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

$\textcolor{g r e e n}{x \approx 0.73}$