Answer
{37}
Work Step by Step
For all positive numbers $a$, where $a\ne1$, and all positive numbers $x$, we know that $y=log_{a}x$ means the same as $x=a^{y}$.
Therefore, $log_{3}(2x+7)=4$ means the same as $3^{4}=2x+7$.
We know that $3^{4}=81$, so we can set $81=2x+7$.
Subtract 7 from both sides.
$2x=74$
Divide both sides by 2.
$x=37$
