Question

find the value of x ​

Answer 1

Step-by-step explanation:

$3^{-5}\cdot \:3^{2x+1}=3^{13}+3^7$

$\frac{3^{-5}\cdot \:3^{2x+1}}{3^{-5}}=\frac{3^{13}}{3^{-5}}+\frac{3^7}{3^{-5}}$

$3^{2x+1}=\frac{3^{13}+3^7}{3^{-5}}$

$3^{2x+1}=387951930$

$\ln \left(3^{2x+1}\right)=\ln \left(387951930\right)$

$\left(2x+1\right)\ln \left(3\right)=\ln \left(387951930\right)$

$x=\frac{\ln \left(129317310\right)}{2\ln \left(3\right)}$

you can check the extended steps here: https://www.symbolab.com/solver/pre-algebra-calculator/3%5E%7B-5%7D%5Ccdot3%5E%7B2x%2B1%7D%3D3%5E%7B13%7D%2B3%5E%7B7%7D