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

Question

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

1757 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-01-10T02:21:40

With powers, the remedy is often logaritms.

Use:
$log(A*B)=logA+logB$ and $logA^B=BlogA$

$log(5x^4)=log(3^x)->$
$log5+4logx=xlog3->$

$color(red)(log5=xlog3-4logx)$

$color(red)(log5=log3^x-logx^4)$

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

and now I'm just going in circles