How do you solve 5^x=30?

Feb 27, 2016

$x \approx 2.11$

Explanation:

$1$. Log both sides of the equation.

${5}^{x} = 30$

$\log \left({5}^{x}\right) = \log \left(30\right)$

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

$x \log \left(5\right) = \log \left(30\right)$

$3$. Solve for $x$ using a calculator.

$x = \log \frac{30}{\log} \left(5\right)$

$\textcolor{g r e e n}{x \approx 2.11}$