Question

Solve the following equations.
$3\sqrt{\log x}+2\log \sqrt{x^{-1}}=2$

Answer 1

$3\sqrt{\log x}+2\log \sqrt{x^{-1}}=2$

$3\sqrt{\log x}=2-2\times \frac{-1}{2}\log x=2+\log x$

$let\log x=z$

$3\sqrt{z}=2+z$

$onsquaring,weget$

$3z=4+z^2+4z$

$z^2-5z+4=0$

$(z-1)(z-4)=04$

$z=1z=4$

$\log x=1\log x=4$

$x=ex=e^4$