# How do you evaluate log_7(343)?

Nov 29, 2015

${\log}_{7} \left(343\right) = 3$

#### Explanation:

If $x = {\log}_{7} \left(343\right)$
then we are looking for a value of $x$ such that ${7}^{x} = 343$

${7}^{1} = 7$
${7}^{2} = 49$
${7}^{3} = 343$

$\Rightarrow x = 3$

In most cases a question like this would require the use of a calculator. In this case the question was obviously set up for a direct solution.

Nov 30, 2015

${\log}_{7} \left(343\right) = {\log}_{7} \left({7}^{3}\right)$
$= 3 {\log}_{7} \left(7\right)$
$= 3 \cdot 1$
$= 3$