# Logarithmic Functions

## Contents

## 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

## Resources

- Logarithmic Functions, Book Chapter
- Guided Notes

## Licensing

Content obtained and/or adapted from:

- Logarithms and Exponentials, Wikibooks: A-level Mathematics/OCR/C2 under a CC BY-SA license