If `x=alpha` satisfies the equation `log_6 (2^(x+3)) - log_6 (3^x - 2) = x`, then find the value of `3^alpha`

Let x=alpha satisfies the equation log_(1/3)(2*((1)/(2))^(x)-1)=log_(1/3)(((1)/(4))^(x)-4) and the value of 8^(alpha) is beta, then find the value of 27 beta.

If alpha and beta are solutions of the equation 4log_(3)^(2)x-4log_(3)x^(2)+1=0 then the value of |(sqrt(alpha beta)+1)/(sqrt(alpha beta)-1)| is

If alpha and beta are roots of equation (log_(3)x)^(2)-4(log_(3)x)+2=0 then The value of alpha beta is

If alpha and beta are roots of equation (log_(3)x)^(2)-4(log_(3)x)+2=0 then The value of alpha beta is

If the root of the equation log_(2)(x)-log_(2)(sqrt(x)-1)=2 is alpha, then the value of alpha^(log_(4)3) is (a) 1 (b) 2 (c) 3 (d) 4

If "log"_(6) (x+3)-"log"_(6)x = 2 , then x =

If "log"_(6) (x+3)-"log"_(6)x = 2 , then x =

If alpha and beta are roots of equation (log_(3)x)^(2)-4(log_(3)x)+2=0 then The value of log_(alpha)beta+log_(beta)alpha is

If alpha and beta are roots of equation (log_(3)x)^(2)-4(log_(3)x)+2=0 then The value of log_(alpha)beta+log_(beta)alpha is

The value of x satisfying the equation 2log_(3)x+8=3.x log_(9)4