# How do you solve 23^x + 5 = 128?

Oct 3, 2016

$x = \ln \frac{123}{\ln} \left(23\right) = {\log}_{23} \left(123\right) \approx 1.535$

#### Explanation:

Using the property that $\ln \left({a}^{x}\right) = x \ln \left(a\right)$, we have

${23}^{x} + 5 = 128$

$\implies {23}^{x} = 123$

$\implies \ln \left({23}^{x}\right) = \ln \left(123\right)$

$\implies x \ln \left(23\right) = \ln \left(123\right)$

$\therefore x = \ln \frac{123}{\ln} \left(23\right) = {\log}_{23} \left(123\right) \approx 1.535$