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. $x$

Answer

Expert–verified

Hide Steps

Answer

Final Answer: $\boxed{1+\log _{2} x}$

Steps

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: $\boxed{1+\log _{2} x}$