Question

Solve for $x$:

$3^{\frac{x}{5}}+3^{\frac{x-10}{10}}=84$.

Answer 1

Now,

$3^{\frac{x}{5}}+3^{\frac{x-10}{10}}=84$

or, ${\left(3^{\frac{x}{10}}\right)}^2+\frac{3^{\frac{x}{10}}}{3}=84$

or, $3.{\left(3^{\frac{x}{10}}\right)}^2+3^{\frac{x}{10}}-3.84=0$

or, $3.{\left(3^{\frac{x}{10}}\right)}^2+{28.3}^{\frac{x}{10}}-{27.3}^{\frac{x}{10}}-3.84=0$

or, $({3.3}^{\frac{x}{10}}+28)(3^{\frac{x}{10}}-9)=0$

We have, $\left({3.3}^{\frac{x}{10}}\right)\ne -28$ so $(3^{\frac{x}{10}}-9)=0$ or, $\frac{x}{10}=2$ or, $x=20$.