# Solve the equation. \log_{x}(16-4x-x^{2})=2

Solve the equation.
${\mathrm{log}}_{x}\left(16-4x-{x}^{2}\right)=2$
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sovienesY
${\mathrm{log}}_{x}\left(16-4x-{x}^{2}\right)=2$
we have to calculate the value of x.
so considering both side as,
${x}^{2}=16-4x-{x}^{2}$
$2{x}^{2}+4x-16=0$
$2{x}^{2}+8x-4x-16=0$
2x(x+4)-4(x+4)=0
(2x-4)-4(x+4)=0
(2x-4)(2x+4)=0

since, negative number cannot be a $\mathrm{log}$ function so we not consider x as -4
so, x=2
The value of ${\mathrm{log}}_{x}\left(16-4x-{x}^{2}\right)=2$ is x=2.