Question

Solve the following equation:
$9^{1+{\log }_{2}x}-3^{1+{\log }_{2}x}-210=0$

Answer 1

$9^{1+{log}_{2}x}-3^{1+{log}_{2}x}-210=0$

Let ${log}_{2}x=a$

$9^{1+a}-3^{1+a}-210=09.(3a{)}^2-3.3^a-210=09.({3a)}^2-45.3^a+42.3^a-210=09.(3^a{)}^2-45.3^a+42.3^a-210=09.3^a(3^a-5)+42(3^a-5)=03^a=5a={log}_{3}5x={}_2{log}_{3}5.$