2.13A

Exponential and Logarithmic Equations

about 35 min · 6 short parts · stop after any part
Solve for xx when it's inside a log or stuck in an exponent.
That's how you answer "how many years until my money triples?" and every log equation on the AP exam.

The path

  1. 1
    Tools you'll use
    You can switch a log to an exponent and spot an illegal log.
  2. 2
    Same log on both sides
    You can solve log⁡aB=log⁡aC\log_a B = \log_a C and throw out bad answers.
  3. 3
    Log equals a number
    You can solve 5+log⁡3(x−2)=75 + \log_3(x - 2) = 7.
  4. 4
    x stuck in an exponent
    You can solve 4e0.2x=204e^{0.2x} = 20 by taking a log.
  5. 5
    Calculator and money
    You can solve by graphing and use A=PertA = Pe^{rt}.
  6. 6
    Tricky cases
    You can spot no-solution cases and solve for a letter.