Study notes
Exponential & Logarithmic Functions
Laws of logarithms, change of base, solving \(a^x=b\) type equations (including quadratic-in-disguise substitutions), and the shapes of \(y=e^x\) and \(y=\ln x\).
What this topic covers
- The three laws of logarithms turn multiplication/division/powers into addition/subtraction/multiplication
- \(\log_a 1 = 0\) and \(\log_a a = 1\), for any valid base \(a\)
- Change of base lets you evaluate a log in whatever base your calculator gives you
- Solving \(a^x=b\) means taking logs of both sides
- An equation with \(a^{2x}\) and \(a^x\) together is a quadratic in disguise
- Combine multiple logs into one before converting to exponential form
- \(y=e^x\) and \(y=\ln x\) are reflections of each other in the line \(y=x\)
Read the full Exponential & Logarithmic Functions notes, free
Sign up free (100% free, no credit card) to unlock the full study notes, worked examples and mind map, and save your child's progress across devices.
Already have an account? Sign in