Logarithm rules

The rules of logarithms are

1. log_a xy = log_a x + log_a y

2. log_a = log_a x – log_a y

3. log_a xⁿ = nlog_a x

4.

Example:

Evaluate 2 log₃ 5 + log₃ 40 – 3 log₃ 10

Solution:

2 log₃ 5 + log₃ 40 – 3 log₃ 10

= log₃ 5² + log₃ 40 – log₃ 10³

= log₃ 25 + log₃ 40 – log₃ 1000

= log₃

= log₃ 1

= 0

Example:

Given that log₂ 3 = 1.585 and log₂ 5 = 2.322, evaluate log₄ 15

Solution:

Have a look at the following videos for more examples on the use of logarithm rules.:

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