# How do you solve the equation 2 log4(x + 7)-log4(16) = 2?

Aug 11, 2016

$x = 9$

#### Explanation:

When working with a log equation, the term must be all logs or all numbers.
Change the RHS to a log term as well.

$\textcolor{red}{2} {\log}_{4} \left(x + 7\right) - {\log}_{4} 16 = {\log}_{4} 16 \text{ } 2 = {\log}_{4} 16$

${\log}_{4} {\left(x + 7\right)}^{\textcolor{red}{2}} - {\log}_{4} 16 = {\log}_{4} 16$

"If logs are being subtracted, the numbers are being divided"

${\log}_{4} \left({\left(x + 7\right)}^{2} / 16\right) = {\log}_{4} 16$

${\left(x + 7\right)}^{2} / 16 = 16 \text{ if log A = log B, A = B}$

${\left(x + 7\right)}^{2} = 256 \text{ cross multiply}$

$x + 7 = 16 \text{ only pos root is valid}$

$x = 9$