# How do you evaluate log_343 (7)?

Sep 23, 2016

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

#### Explanation:

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

Step 1: Rewrite as an exponential.
${343}^{x} = 7$

Step 2:Take the log of both sides.
$\log {343}^{x} = \log 7$

Step 3: Use the log rule $\log {a}^{x} = x \log a$.
$x \log 343 = \log 7$

$x = \log \frac{7}{\log} 343 \textcolor{w h i t e}{a a a a}$Use a calculator
$x = \frac{1}{3}$

OR

Use the change of base formula ${\log}_{b} a = \log \frac{a}{\log} b$
${\log}_{343} \left(7\right) = \log \frac{7}{\log} 343 = \frac{1}{3} \textcolor{w h i t e}{a a a}$ Use a calculator

OR

Rewrite as an exponential and consider the powers of 7.
${343}^{x} = 7$

$343 = {7}^{3}$ or $\sqrt[3]{343} = 7$ or ${343}^{\frac{1}{3}} = 7$
$x = \frac{1}{3}$