# How do you solve log_7x=log_2 9?

Mar 25, 2016

$x = 477.59$

#### Explanation:

As ${\log}_{b} x = {\log}_{a} \frac{x}{\log} _ a b$, we have

${\log}_{7} x = {\log}_{2} 9$ is ${\log}_{10} \frac{x}{\log} _ 10 7 = {\log}_{10} \frac{9}{\log} _ 10 2$ i.e.

$\log \frac{x}{\log} 7 = \log \frac{9}{\log} 2$

Hence $\log x = \frac{\log 9 \cdot \log 7}{\log} 2 = \frac{0.9542 \cdot 0.8451}{0.3010}$ or

$\log x = 2.679$ or $x = {10}^{2.679}$ or

$x = 477.59$