Question

Solve the following equations.
$log(3x-2)-2=\frac{1}{2}log(x+2)-log50.$

Answer 1

$log(3x-2)-2=\frac{1}{2}log(x+2)-log50\Rightarrow \log \frac{3x-2}{\sqrt{x+2}}=log2$

according to domain x must be >2/3

therefore solving the equation

$\frac{3x-2}{\sqrt{x+2}}=2thereforex=2,\frac{-2}{9}$

therefore the solution is $x=2$