Question

match the logarithmic function with its graph.
$f(x)=\log_{3}x$
$f(x)=\log_{4}x$

Explanation:

Step1: Recall log function properties

For $f(x)=\log_b x$, when $b>1$, the function is increasing, and passes through $(1,0)$. Larger $b$ means slower growth for $x>1$.

Step2: Compare growth rates

• For $f(x)=\log_2 x$: At $x=4$, $f(4)=\log_2 4=2$.
• For $f(x)=\log_4 x$: At $x=4$, $f(4)=\log_4 4=1$.

Step3: Match to graphs

The upper graph reaches a higher value at $x=4$, so it corresponds to the faster-growing $\log_2 x$. The lower graph corresponds to $\log_4 x$.

Answer:

Upper graph $\longleftrightarrow f(x)=\log_{2}x$
Lower graph $\longleftrightarrow f(x)=\log_{4}x$