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.
