FUN016 · Functions & graphs · Classes 11–12
Logarithmic Function
The logarithmic function y = log_b x is the inverse of y = bˣ. Its graph is the exponential graph reflected in y = x; it passes through (1, 0).
log_b xLogarithmic Function
📐 Formula
f(x) = log_b x, x > 0; asymptote x = 0
✏️ Worked example
b = 2: log₂ 8 = 3, because 2³ = 8.
🌍 Where it is used
Measuring orders of magnitude: decibels, pH, star brightness.
❓ Quick check
log₂ 16 = ?
🏋️ Practice
Easylog₃ 9 = ?
Answer: 2
MediumWhat is the domain of y = log x?
Answer: x > 0
ChallengeSolve log₂(x − 1) = 3.
Answer: x = 9