Question

Solve the following equations.
$x^{logx-3}=\mathrm{0.01.}$

Answer 1

$x^{logx-3}=0.01$

Applying log on both sides

$[log\left(x\right)-3]log\left(x\right)=log\left(0.01\right)$

${\left(log\left(x\right)\right)}^2-3log\left(x\right)=log\left(100\right)$

${\left(log\left(x\right)\right)}^2-3log\left(x\right)=-2$

${\left(log\left(x\right)\right)}^2-3log\left(x\right)+2=0$

${\left(log\left(x\right)\right)}^2-2log\left(x\right)-log\left(x\right)+2=0$

$log\left(x\right)(log\left(x\right)-2)-1(log\left(x\right)-2)=0$

$log\left(x\right)=1$ or $log\left(x\right)=2$

$x=10$ or $x={10}^2$

$x=100$