Exponential and Logarithmic Functions Topic Review summary

Key learning points

• $y=e^x$ and $y=\ln x$ are inverses; domains/ranges swap.
• Laws of logs still drive equation solving.
• Change of base and natural logs appear in calculus setups.
• Solve mixed exponential equations by taking $\ln$.
• Asymptotes: $y=0$ for exponentials; $x=0$ for $\ln x$.

Worked example 1 — Solve

$e^{2x}=7$.

Working

Take $\ln$.

Worked example 2 — Cancel

Simplify $\ln(e^{3x})$.

Working

Inverse functions.

Worked example 3 — y=e^x and y=\\ln x are inverses; domains/r

$y=e^x$ and $y=\\ln x$ are inverses; domains/ranges swap.

Working

Attempt without notes, then check the answers PDF.

Worked example 4 — Laws of logs still drive equation solving

Apply this idea from the Topic Review: Laws of logs still drive equation solving.

Working

Attempt without notes, then check the answers PDF.

Scaffolded Learning Sheet and answers (PDFs)

This page is a short, searchable overview for revision and search engines. Use the Scaffolded Learning Sheet first, then the Answers PDF for a full written solution. The printable PDFs remain the main classroom resource.