How do you solve $log5^(2x) = 4$ ?

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Answer 1 · 2015-11-04T17:39:17

The solution is $x=2/log(5)$

A property of lohgarithms states that

$log(a^b)=blog(a)$

In your case, $a=5$ and $b=2x$ , so the equality becomes

$log(5^{2x})=2xlog(5)$ .

At this point, it's very easy to isolate the $x$ , since $log(5)$ is just a number, and we have

$log(5^{2x}) = 4$

$iff$

$2xlog(5)=4$

$iff$

$x=4/(2log(5)) = 2/log(5)$

How do you solve log5^(2x) = 4log5^(2x) = 4?