Question

(log x)^2 =  logx^2 How would you solve this math question?

Answer 1

The logarithmic equation (logx)² = logx²

(logx)(logx) = logx²

{ Apply the power property : log a^m = m log a}

(logx)(logx) = 2logx

(logx)(logx) - 2logx = 0

logx[ logx - 2] = 0

Apply zero product property.

logx = 0 and logx - 2 = 0

Solve logx = 0

x = 10⁰

x = 1

Now solve  logx - 2 = 0

logx = 2

x = 10²

x = 100

Solutions are x = 1 and x = 100.