# How do you solve log_x 1000=3?

Jul 13, 2016

x = 10

#### Explanation:

Using $\textcolor{b l u e}{\text{law of logarithms}}$

$\textcolor{\mathmr{and} a n \ge}{\text{Reminder}}$

$\textcolor{red}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{{\log}_{b} x = n \Leftrightarrow x = {b}^{n}} \textcolor{w h i t e}{\frac{a}{a}} |}}}$

Relating to the given question.

x = 1000 , b = x and n = 3

$\Rightarrow 1000 = {x}^{3} \Rightarrow {10}^{3} = {x}^{3} \Rightarrow x = 10$