Problem
Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. \[ \log _{2}(2 x) \] A. 2 B. $1+\log _{2} x$ C. 1 D. $x$
Solution
Step 1 ：Given the logarithmic expression \(\log _{2}(2 x)\).
Step 2 ：Use the property of logarithms that states \(\log_b(mn) = \log_b(m) + \log_b(n)\) to rewrite \(\log_2(2x)\) as \(\log_2(2) + \log_2(x)\).
Step 3 ：We know that \(\log_2(2) = 1\), so the expression simplifies to \(1 + \log_2(x)\).
Step 4 ：Final Answer: \(\boxed{1+\log _{2} x}\)
