Question

1. label the curves with the correct function names. $f(x) = \log_{2} x, g(x) = \log_{3} x, \text{and } h(x) = \log_{8} x$

dashed:
dotted:
solid:

Explanation:

For logarithmic functions $\log_b x$, as the base $b$ increases, the graph grows more slowly for $x>1$. We can test a common $x$-value, e.g., $x=8$:

• $f(8)=\log_2 8=3$
• $g(8)=\log_3 8\approx1.89$
• $h(8)=\log_8 8=1$

The highest curve at $x=8$ is the dashed line, the middle is dotted, the lowest is solid.

Answer:

dashed: $f(x)=\log_2 x$
dotted: $g(x)=\log_3 x$
solid: $h(x)=\log_8 x$