Question

the graph of $f(x) = \log_{2}(2x)$ is shown below.
use the graph to express $f(x)$ in terms of $\log_{2}(x)$.

Explanation:

Step1: Recall Logarithm Property

Use the logarithm product rule: $\log_b(ac) = \log_b(a) + \log_b(c)$. For $f(x)=\log_2(2x)$, apply the rule: $\log_2(2x)=\log_2(2)+\log_2(x)$.

Step2: Evaluate $\log_2(2)$

Since $2^1 = 2$, $\log_2(2) = 1$. Substitute this into the expression: $\log_2(2x)=1+\log_2(x)$.

Answer:

$f(x) = 1 + \log_2(x)$