# How do you solve the equation log_x 243=5?

Nov 25, 2016

$x = 3$

#### Explanation:

question given
solve $\setminus {\log}_{x} \left(243\right) = 5$

concept applied
log to exponential conversion $y = {x}^{b} \setminus \leftrightarrow b = \setminus {\log}_{x} \left(y\right)$

• the equation is in the form of $\setminus \textcolor{red}{x = {\log}_{b} \left(y\right)}$

calculation
let's convert to $\setminus \textcolor{g r e e n}{y} = {x}^{\setminus} \textcolor{b l u e}{b}$ form.

• in the equation you are given, $\setminus \textcolor{b l u e}{b = 5}$, $\setminus \textcolor{g r e e n}{y = 243}$, and you need to find the value for $x$.
• putting this into the equation:
$\setminus \textcolor{g r e e n}{243} = {x}^{\setminus} \textcolor{b l u e}{5}$
• after this you would either find the fifth root of 243, or you can use a calculator to plug in values.