To be exact, I have a few questions on logarithms.. The questions are listed as follow. It would be great if you could show necessary workings and solution.

Question 1

Prove that the equation has a real root from the root x=2. Find this root.

2^(2x) + 64[2^(-2)] =32

Question 2

Given that 2y = a^x + a^(-x) where a>1 and x>0

Prove that a^x = y + (y^2 -1)^1/2

Similarly if 2z = a^(3x) = a^(-3x) prove that z=4y^3 -3y

Question 3

Solve the equation

5/(x+1)^1/2 -3 (x+1)^1/2 + 2 = 0