Question

1. label the graphs with the correct function names $f(x) = \log_{4} x, g(x) = \log_{6} x, or \\ h(x) = \log_{12} x$.

a:
b:
c:

Explanation:

For logarithmic functions of the form $y=\log_b x$ where $b>1$, the larger the base $b$, the slower the function grows for $x>1$, and the closer the curve is to the $x$-axis for $x>1$. All these functions pass through the point $(1,0)$.

1. For graph A (the steepest curve for $x>1$), it corresponds to the smallest base, so it is $f(x)=\log_4 x$.
2. For graph B, it has a moderate slope, so it corresponds to the middle base, $g(x)=\log_6 x$.
3. For graph C (the flattest curve for $x>1$), it corresponds to the largest base, $h(x)=\log_{12} x$.

Answer:

A: $f(x)=\log_4 x$
B: $g(x)=\log_6 x$
C: $h(x)=\log_{12} x$