#### Answer

(a) It is defined as the inverse function of the exponential function.
(b) The domain of this function is $(0,\infty)$.
(c) The range of this function is $(-\infty,\infty)$.
(d) This shape is shown on the graph below.

#### Work Step by Step

(a) It is defined as the inverse function of the exponential function i.e. as the solution of the equation
$$a=b^x\Rightarrow x=\log_ba.$$
where $b$ is the basis for both the exponential function and the logarithm.
(b) The domain of this function is the range of the exponential function i.e. the set of all positive reals $(0,\infty)$.
(c) The range of this function is the domain of the exponential function i.e. it is the set of all reals $(-\infty,\infty)$.
(d) This shape is obtained by reflecting the exponential function with $b>1$ about $x=y$ and it is shown on the figure bellow.