Question

Find the value of $x$, if ${\log }_{4}8+{\log }_4(x+3)-{\log }_4(x-1)=2$

Answer 1

$x+3>0andx-1>0$

${\log }_{4}8+{\log }_4(x+3)-{\log }_4(x-1)=2$
$\Rightarrow$ ${\log }_4\frac{8(x+3)}{x-1}=2[\because a\log x=\log x^a\text{\&}\log a+\log b+\log c=\log (abc\left)\right]$
$\Rightarrow$ $\frac{8(x+3)}{x-1}=4^2$
$\Rightarrow$ $x+3=2x-2$
$\Rightarrow x=5$
Ans: 5