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Curriculum · Algebra · Functions

Logarithms

Logs as inverse exponentials; the identities and the classic contest patterns.

Objectives

  • Convert between exp and log form
  • Apply log identities
  • Solve log equations

The full interactive edition of this lesson ships in v1.5. The topic is live everywhere else — the problems below feed your Functions mastery now.

Train the topic

●●○○○If f(x)=2x+3f(x) = 2x + 3, what is f(f(2))f(f(2))?AMC 10 style●●●○○What is the minimum value of f(x)=x2−4x+7f(x) = x^2 - 4x + 7?AMC 10 style●●●○○Solve for xx: log⁡2x+log⁡2(x−2)=3\log_2 x + \log_2 (x - 2) = 3.AMC 12 style