# How do you solve 3^(2x+1)=5^200?

Apr 30, 2016

$\implies x = \frac{200 \log 5 - \log 3}{2 \log 3}$

#### Explanation:

${3}^{2 x + 1} = {5}^{200}$

Taking log on both sides we have

$\log \left({3}^{2 x + 1}\right) = \log \left({5}^{200}\right)$

$\implies \left(2 x + 1\right) \log \left(3\right) = 200 \log \left(5\right)$

$\implies 2 x \log 3 + \log 3 = 200 \log 5$

$\implies 2 x \log 3 = 200 \log 5 - \log 3$

$\implies x = \frac{200 \log 5 - \log 3}{2 \log 3}$