Question

Solve $9^{1+\log x}-3^{1+\log x}-210=0,$ where base of log is 3.

Answer 1

$let{3}^{1+\log x}=z$

$z^2-z-210=0$

$z^2-15z+14z-210=0$

$z(z-15)+14(z-15)=0$

$(z+14)(z-15)=0$

$z=15,z=-14$

$now,z=15$

$3^{1+\log x}=15$

$1+{\log }_{3}x={\log }_{3}15$

${\log }_{3}x={\log }_3\left(\frac{15}{3}\right)$

${\log }_{3}x={\log }_{3}5$

$x=5$