Answer
Please see image
.
Work Step by Step
The function $g(x)=\log_{b}x$ (the logarithmic function with base $b$)
is the inverse function of the exponential function with base $b,\ f(x)=b^{x}$
The graphs of inverse functions are reflections of the original function,
about the line y=x.
The base b here is $\displaystyle \frac{1}{4}=0.25.$
Our plan:
1. graph f(x) by plotting several points, (x,f(x))
joining them with a smooth curve,
2. swap the coordinates of the points we got in step 1
to obtain new points (f(x),x).
3. The points in (2.) are reflections of the points in (1.) about the line y=x.
We may graph the line y=x to illustrate this.
Joining this new set of points, we have graphed g(x)
