Exponentials and logarithms

Topic practice · Paper 1 · Core

This free ExamAlly page is a TMUA exponentials and logarithms practice question for students preparing for the TMUA (Test of Mathematics for University Admission). Use it to check your understanding of Exponentials and logarithms, attempt every option under light time pressure, then read the full worked solution.

Independent practice material, not affiliated with official TMUA organisers.

Matching revision guide: Read the Exponentials & logs TMUA revision guide

Let $C$ be the curve $y=a^x$ with $a>0$ , $a \neq 1$ . Curve $D$ is obtained by reflecting $C$ in the $y$ -axis and then translating it upward by 2 units, so $D$ has equation $y=a^{-x}+2$ . For which values of $a$ do $C$ and $D$ intersect at exactly one point?

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