`(a^(log_b x))^2-5x^(log_b a)+6=0`

If (a^(log_b x))^2-5 a^(log_b x)+6=0, where a >0, b >0 & a b!=1, then the value of x can be equal to (a) 2^(log_b a) (b) 3^(log_a b) (c) b^(log_a2) (d) a^(log_b3)

If b gt 1, x gt 0 and (2x)^(log_(b) 2)-(3x)^(log_(b) 3)=0 , then x is

If b gt 1, x gt 0 and (2x)^(log_(b) 2)-(3x)^(log_(b) 3)=0 , then x is

Prove that 1/(log_(a/b) x)+1/(log_(b/c) x)+1/(log_(c/a) x)=0

Prove the following identities: (a) (log_(a) n)/(log_(ab) n) = 1+ log_(a) b" "(b) log_(ab) x = (log_(a) x log_(b) x)/(log_(a) x + log_(b) x) .

Prove the following identities: (a) (log_(a) n)/(log_(ab) n) = 1+ log_(a) b" "(b) log_(ab) x = (log_(a) x log_(b) x)/(log_(a) x + log_(b) x) .

Prove the following identities: (a) (log_(a) n)/(log_(ab) n) = 1+ log_(a) b" "(b) log_(ab) x = (log_(a) x log_(b) x)/(log_(a) x + log_(b) x) .

Prove the following identities: (a) (log_(a) n)/(log_(ab) n) = 1+ log_(a) b" "(b) log_(ab) x = (log_(a) x log_(b) x)/(log_(a) x + log_(b) x) .

Assuming that all logarithmic terms are define which of the following statement(s) is/are incorrect? (A)log_b(ysqrtx)=log_b y.(1/2log_b x) , (B) log_b x-log_b y=(log_b x)/(log_b y) , (C)2(log_b x+log_b y)=log_b (x^2y^2) , (D) 4log_b x-log_b y=log(x^4/y^-3)

Q. If log_x a, a^(x/2) and log_b x are in G.P. then x is equal to (1) log_a(log_b a) (2) log_a(log_e a)+log_a log_b b (3) -log_a(log_a b) (4) none of these