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Grade 11 Math Lab: Transcendence & Limits FREE

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Logarithmic Functions

60 min Grade 11 Math Lab: Transcendence & Limits

Learning Objectives

  • Convert between log and exponential forms
  • Apply log properties
  • Solve log equations

Key Concepts

Logarithm

log_b(x) = y means b^y = x

Common Log

log(x) = log₁₀(x)

Natural Log

ln(x) = logₑ(x)

Theory

**log_b(x) = y ⟺ b^y = x** **Properties:** - log_b(MN) = log_b(M) + log_b(N) - log_b(M/N) = log_b(M) - log_b(N) - log_b(M^n) = n·log_b(M) - log_b(1) = 0, log_b(b) = 1 **Change of Base:** log_b(x) = ln(x)/ln(b)

Examples

Solve: log₂(x) = 5

Solution: x = 2⁵ = 32