Prove that :
`a^(log_x b) = b^(log_x a)`

Prove that m^(log_(a)x)=x^(log_(a)m)

Prove that: log_(a)x xx log_(b)y=log_(b)x xx log_(a)y

Prove that: log_(a)x=log_(b)x xx log_(c)b xx...xx log_(n)m xx log_(a)n

Prove that: (log_(a)(log_(b)a))/(log_(b)(log_(a)b))=-log_(a)b

Prove that log_(ab)(x)=((log_(a)(x))(log_(b)(x)))/(log_(a)(x)+log_(b)(x))

If a,b,c are in G.P.,prove that: log_(a)x,log_(b)x,log_(c)x are in H.P.

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)

Prove that a sqrt(log_(a)b)-b sqrt(log_(b)a)=0

If a^(2) + b^(2) = 7 ab," prove that " log((a+b)/3) = 1/2 (log a + log b) .

If y^(2)=xz and a^(x)=b^(y)=c^(z), then prove that (log)_(a)b=(log)_(b)c