How do you solve log x + log 3 = log 21?

Dec 18, 2015

$\textcolor{w h i t e}{\times} \implies x = 7$

Explanation:

$\textcolor{w h i t e}{\times} \log x + \log 3 = \log 21$

The sum of the logarithms is the logarithm of a product of the numbers being added:

$\textcolor{w h i t e}{\times} \textcolor{red}{\log \left(3 x\right)} = \log 21$
$\implies \textcolor{red}{\frac{1}{3} \times} 3 x = \textcolor{red}{\frac{1}{3} \times} 21$
$\implies x = 7$