# Can 5x^4=3^x be solved algebraically?

## I solved a problem similar to this using graphing but are there algebra techniques for solving an equation of this form?

Jan 10, 2017

With powers, the remedy is often logaritms.

#### Explanation:

Use:
$\log \left(A \cdot B\right) = \log A + \log B$ and $\log {A}^{B} = B \log A$

$\log \left(5 {x}^{4}\right) = \log \left({3}^{x}\right) \to$
$\log 5 + 4 \log x = x \log 3 \to$

$\textcolor{red}{\log 5 = x \log 3 - 4 \log x}$

$\textcolor{red}{\log 5 = \log {3}^{x} - \log {x}^{4}}$

color(red)(log5=log(3^x/x^4)

and now I'm just going in circles