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Grade 11 Math Lab: Transcendence & Limits FREE
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Logarithmic Functions
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