MATHEMATICS · Multi-part · A Level · Mathematics · Exponentials and logarithms · Exponentials and logarithms
Problem
The curves y=3x and y=log3x are drawn on the same set of axes. Answer the following:
(i) Prove that each of the two given functions is the inverse of the other.
(ii) Using the result of part (i), deduce the domain and the range of each function.
(iii) Determine all intercepts and asymptotes of both curves.
(iv) Show algebraically that the graphs of the two functions are reflections of each other about the line y=x.