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.
Prove that the equation has a real root from the root x=2. Find this root.
2^(2x) + 64[2^(-2)] =32
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
Solve the equation
5/(x+1)^1/2 -3 (x+1)^1/2 + 2 = 0