Exponential & Logarithmic Functions

What you'll learn

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 \(y=\ln x\).

• 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 \(y=x\)