# How do you solve  log_3(47) = log_8(x)?

Aug 7, 2018

$x = 1462.514$

#### Explanation:

As ${\log}_{3} 47 = {\log}_{8} x$, we have

$\log \frac{47}{\log} 3 = \log \frac{x}{\log} 8$

or $\log x = \log \frac{47}{\log} 3 \times \log 8$

or $\log x = \frac{16721}{0.4771} \times 0.9031 = 3.1651$

and $x = {10}^{3.1651} = 1462.514$