Logarithmic Functions

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Logarithmic Functions


In mathematics you can find the inverse of an exponential function by switching x and y around: becomes . The problem arises on how to find the value of y. The logarithmic function solved this problem. All conversions of logarithmic function into an exponential function follow the same pattern: becomes . If a log is given without a written b then b=10. Also with logarithmic functions, b > 0 and . There are 2 cases where the log is equal to x: and .

To recap, a logarithm is the inverse function of an exponent.

e.g. The inverse of the function is .

In general, , given that .

Laws of Logarithmic Functions

When X and Y are positive.

Change of Base

When x and b are positive real numbers and are not equal to 1. Then you can write as . This works for the natural log as well. here is an example:

Solving a Logarithmic Equation

A logarithmic equation is an equation wherein one or more of the terms is a logarithm.

e.g. Solve ( is another way of writing ).

now check



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