# How do you solve Log x = 5 Log 4?

Mar 19, 2016

$x = 1024$

#### Explanation:

$1$. Use the log property, ${\log}_{\textcolor{p u r p \le}{b}} {\textcolor{red}{m}}^{\textcolor{b l u e}{n}} = \textcolor{b l u e}{n} \cdot {\log}_{\textcolor{p u r p \le}{b}} \textcolor{red}{m}$, to rewrite $5 \log 4$.

$\log x = 5 \log 4$

$\log x = \log {4}^{5}$

$2$. Since the equation now follows a "$\log = \log$" situation, where the bases are the same on both sides, rewrite the equation without the "log" portion.

$x = {4}^{5}$

$3$. Solve for $x$.

$\textcolor{g r e e n}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} x = 1024 \textcolor{w h i t e}{\frac{a}{a}} |}}}$