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Basic Properties of Logarithms

Writer's picture: Sean Melvein A. VecinaSean Melvein A. Vecina

Let b and x be real numbers such that b > 0 and b must not be equal to one. The basic properties of logarithms are as follows:


  1. logb 1 = 0

Examples:

log100 1 = 0

log1000 1 = 0

log50 1 = 0

2. logb b^x = x

Examples:

log5 5^3 = 3

log6 6^2 = 2

log 10^5 = 5


3. If x > 0, then b^logb x = x

Examples:

3^log3 5 = 5

4^log4 8 = 8

7^log7 2 = 2




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