# How do you use logarithms to solve for x in 5^(x+1)=24?

Jul 12, 2018

$\textcolor{b l u e}{x \approx 0.974635869}$

#### Explanation:

${5}^{x + 1} = 24$

Taking logarithms of both sides:

$\ln \left({5}^{x + 1}\right) = \ln \left(24\right)$

Form the laws of logarithms:

$\log \left({a}^{b}\right) = b \log \left(a\right)$

$\left(x + 1\right) \ln \left(5\right) = \ln \left(24\right)$

Divide by $\ln \left(5\right)$

$x + 1 = \ln \frac{24}{\ln} \left(5\right)$

$x = \ln \frac{24}{\ln} \left(5\right) - 1 \approx 0.974635869$