Logarithms

Logarithms can be considered as the inverse of indices.

If a^x = y such that a > 0, a ≠ 1 then log_a y = x

a^x = y ↔ log_a y = x

Take note of the following:

• Since a¹ = a, log_a a = 1
• Since a⁰ = 1, log_a 1 = 0
• Log_a 0 is undefined
• Logarithms of negative numbers are undefined.
• The base of logarithms can be any positive number except 1.
• Logarithms to the base 10 are known as common logarithms and are represented by log₁₀ or lg.

Example:

Calculate the value of each of the following:

a) 1og₂ 64

b) log₉ 3

Solution:

a) Let x = log₂ 64
2^x = 64
x = 6

b) Let x = log₉ 3
9^x = 3
x =

Have a look at the following video for more examples on solving logarithms.:

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