How do you solve $5^{2 x} = 20$ $5^(2x)=20$ ?

Question

9824 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-05-04T00:56:29

The solution is $x = \frac{{log}_{5} (20)}{2}$ $x=log_5(20)/2$ .

To solve the equation, take the ${log}_{5}$ $log_5$ of both sides:

$5^{2 x} = 20$ $5^(2x)=20$

${log}_{5} (5^{2 x}) = {log}_{5} (20)$ $log_5(5^(2x))=log_5(20)$

$color(red)cancelcolor(black)(log_5)(color(red)cancelcolor(black)5^(2x))=log_5(20)$

$2x=log_5(20)$

$x=log_5(20)/2$

$color(white)x~~0.930677...$

Hope this helped!

How do you solve 5^(2x)=2052x=205^(2x)=20?