What Is a Logarithm?

A logarithm is a type of function. There are multiple types of logarithms, but here we are looking at common logarithms.

Theory

The Common Logarithm

The common logarithm is also known as the decadic logarithm. It looks like this

log(x),x > 0

It can also be written like this:

logx lg(x) lg x

Theory

The Common Logarithm and the Number 10

These are some of the rules you use when solving logarithmic equations.

10logx = xlog 10x = x

Logarithms can seem a bit odd, but they are just a special definition of a number: The logarithm to the number x is the number n that you have to use so that 10n = x

Like this:

log 1 = 0 because 100 = 1 log 100 = 2 because 102 = 100 log 0.001 = 3 because 103 = 0.001

Example 1

Solve the logarithmic equation logx = 4

logx = 4 10logx = 104 x = 10000

Example 2

Solve the equation 10x = 3000

10x = 3000 log 10x = log 3000 x 3.477

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