Math11: Chapter 4- Exponentials and logarithms

Converting from index form to logarithmic form and vice versa

Defination of Logarithms.

Suppose b>0 and b≠1,there is a number ‘x’such that

a ^b = c ↔ log_a c = b

where a is called as base

b is called as log

Say " log c to the base a is b

For example : 10² = 100 ↔ log₁₀100 = 2

Q1: Write 4² = 16 in logarithmic form.

Solution :

log₄16=2

Q2: Write log₃81=4 in exponential form.

Solution: 3⁴=81

Logarithmic Rules

Example:

Q1: Express the given expression in terms of

loga, logb and logc.

Solution:

By rule 2

By rule 1

By rule 3

Q2: Express as a single log.

Solution :

Solve:

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