# How do you solve 7^(2x-3) - 4 = 14?

Apr 6, 2016

You must work with the fact that ${a}^{n} = m \to \log {a}^{n} = \log m$

#### Explanation:

${7}^{2 x - 3} = 18$

$\log {7}^{2 x - 3} = \log 18$

Simplify using the rule $\log {a}^{n} = n \log a$

$\left(2 x - 3\right) \log 7 = \log 18$

$2 x \log 7 - 3 \log 7 = \log 18$

$2 x \log 7 = \log 18 + 3 \log 7$

Use the rule ${\log}_{a} n + {\log}_{a} m = {\log}_{a} \left(n \times m\right)$

$x \left(2 \log 7\right) = \log \left(18 \times 343\right)$

$x = \log \frac{6174}{\log} 49$

$x = 2.24$