Year 9
Mathematics
Algebra
AC9M9A02
Laws of Logarithms
Logarithms are the inverse of exponential functions. log_a(x) = y means a^y = x. The laws of logarithms simplify calculations involving products, quotients, and powers.
What You Need to Know
Key Concept Diagram
log_a(xy) = log_a(x) + log_a(y) (product law)
log_a(x/y) = log_a(x) - log_a(y) (quotient law)
log_a(x^n) = n log_a(x) (power law)
log_a(a) = 1 and log_a(1) = 0
Key Vocabulary
Logarithm
The exponent to which a base must be raised to produce a given number
Base
The number that is raised to a power in a logarithmic expression
Product law
log(xy) = log(x) + log(y)
Power law
log(x^n) = n log(x)
Knowledge Check
Select the correct answer for each question. Click "Check Answer" to see if you are right.
Question 1
Evaluate log_2(8).
Question 2
Simplify log_3(9) + log_3(3).
Question 3
Simplify log_5(x^4) using the power law.
Key Concepts Summary
- ●log_a(xy) = log_a(x) + log_a(y) (product law)
- ●log_a(x/y) = log_a(x) - log_a(y) (quotient law)
- ●log_a(x^n) = n log_a(x) (power law)
- ●log_a(a) = 1 and log_a(1) = 0