# How do you solve 7^(2x-1) = 343?

Mar 12, 2016

$x = 2$

#### Explanation:

We will use the following properties of logarithms:

• ${\log}_{a} \left(a\right) = 1$
• $\log \left({a}^{x}\right) = x \log \left(a\right)$

${7}^{2 x - 1} = 343 = {7}^{3}$

${\log}_{7} \left({7}^{2 x - 1}\right) = {\log}_{7} \left({7}^{3}\right)$

$\left(2 x - 1\right) {\log}_{7} \left(7\right) = 3 {\log}_{7} \left(7\right)$

$2 x - 1 = 3$

$2 x = 4$

$x = 2$