The product of all the real solution(s) of the equation 2 log 9(x-1)=2+ log (x-1)2 3- log √3(x-1) is

Question

The product of all the real solution(s) of the equation 2 log 9(x-1)=2+ log (x-1)2 3- log √3(x-1) is (A) 3 (B) 4 (C) 40 (D) (4/3)

Tardigrade Admin · Accepted Answer

Let t = log 3( x -1) Hence, t=2+(1/t2)-2 t ⇒ 3 t=(2 t2+1/t2) ⇒ 3 t3-2 t2-1=0 ⇒(t-1)(3 t2+t+1)=0 Hence, t=1 ⇒ log 3(x-1)=1 ⇒ x=4

Q. The product of all the real solution(s) of the equation $2 lo g_{9} (x - 1) = 2 + lo g_{(x - 1)}^{2} 3 - lo g_{3} (x - 1)$ is