Answer
Please see step-by-step.
Work Step by Step
(See pages 344-345)
The logarithmic function $\log_{a}$ with base $a ($where $a>0, a\neq 1)$
is defined for $x>0$ by
$\log_{a}x=y \Leftrightarrow a^{y}=x$
So, $\log_{a}x$ is the exponent to which the base $a$ must be raised to give $x$.
a.
The domain of $\log_{a}$ is $(0, \infty)$, and
b.
the range is $\mathbb{R}$.
c.
For $a>1$, the shape of the graph of the function $\log_{a}$ is given with the RED graph in Figure 2 (p. 345)
Key characteristics:
- passes through (1,0), grows without bound to the right of x=1,
- negative for $x < 1$, zero for $x=1,$ positive for $x > 1,$
- when x approaches zero, the logarithm is negative and becomes large in magnitude
- it is the mirror image of the exponential graph, over the line $y=x.$
