#### Answer

$log_{343}7=\frac{1}{3}$

#### 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, $\sqrt[3] 343=343^{\frac{1}{3}}=7$ means the same as $log_{343}7=\frac{1}{3}$.