Question

both logs have base 2.
log(X)^2=(log(x))^2
I have never come across a question where I need to square the log can anybody help

Answer 1

\(\log_2 x^2 = \log_2^2 x\)

\(2 \log_2 x = \log_2^2 x\)

\(\log_2^2 x - 2 \log_2 x = 0\)

\(\log_2 x(\log_2 x - 2) =0\)

\(\log_2 x = 0 \) or \(\log_2x = 2\)

\(x = 1\) or \(x = 4\)

Answer 2

Solve it as a quadratic in \(\log_2 x\).
Then solve the log parts for x.