# How do you solve the equation log_3 5+log_3 x=log_3 10?

Nov 20, 2016

${\log}_{3} 5 + {\log}_{3} x = {\log}_{3} 10$

${\log}_{3} x = {\log}_{3} 10 - {\log}_{3} 5$

Use the subtraction rule of logarithms: ${\log}_{a} n - {\log}_{a} m = {\log}_{a} \left(\frac{n}{m}\right)$.

${\log}_{3} x = {\log}_{3} \left(\frac{10}{5}\right)$

${\log}_{3} x = {\log}_{3} 2$

If $\log a = \log b$, then $a = b$.

$x = 2$

Hopefully this helps!