If `y=a^(1/(1-(log)_a x))` and `z=a^(1/(1-(log)_a y))`,then prove that `x=a^(1/(1-(log)_a z))`

If y= 2^((1)/(log_(x)4)) then prove that x=y^(2) .

If (log)_a3=2 and (log)_b8=3 , then prove that (log)_a b=(log)_3 4.

Prove that ln(1+x) 0.

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

If f(x)=log[(1+x)/(1-x)], then prove that f[(2x)/(1+x^2)]=2f(x)dot

If ("log"x)/(y - z) = ("log" y)/(z - x) = ("log" z)/(x - y) , then prove that xyz = 1.

If x=(log)_(2a)a , y=(log)_(3a)2a ,z=(log)_(4a)3a ,prove that 1+x y z=2y z

Simplify: 1/(1+(log)_a b c)+1/(1+(log)_b c a)+1/(1+(log)_c a b)

Draw the graph of y=1/(log_(e)x)

If 3^x=4^(x-1) , then x= (2(log)_3 2)/(2(log)_3 2-1) (b) 2/(2-(log)_2 3) 1/(1-(log)_4 3) (d) (2(log)_2 3)/(2(log)_2 3-1)