Chapter 8 · ICSE Class 9 Mathematics (Selina Concise)

Logarithms

Understand logarithms as the inverse of exponents, and apply the laws of logarithms to simplify expressions.

📊 Chapter 8

The relationship between exponential form and logarithmic form The equation 2 to the power 3 equals 8 shown alongside its equivalent logarithmic form, log base 2 of 8 equals 3 2³ = 8 is the same as log₂ 8 = 3
8.1

What is a Logarithm

logₐN=x means aˣ=N. A logarithm answers the question: to what power must the base be raised to get N?

1

Find log₂8.

2³=8, so log₂8=3

2

Find log₁₀1000.

10³=1000, so log₁₀1000=3

8.2

Laws of Logarithms

log(mn)=log m+log n, log(m/n)=log m−log n, and log(mⁿ)=n log m. These laws simplify complex logarithmic expressions.

1

Simplify: log 5 + log 2

log(5×2)=log 10=1

2

Simplify: log 100 − log 10

log(100/10)=log 10=1

Practice

Exercises

1. Find log₃27.

2. Find log₁₀10000.

3. Simplify: log 4 + log 25

4. Simplify: log 50 − log 5

5. Simplify: log₂32

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