## Logarithmic and Exponential Laws

These are important to know both for when we are graphing these functions and algebraically solving these equations.

## Exponential Equations

First we will look at exponential equations and the first rule.

### Index Laws

Here are a few of index laws, which are used to solve exponential equations:

### Exponential Example

2013 exam 1 Question 5 b

**Solve ****, for x**

Our first step is to make the base numbers the same

Then we can equate the powers and solve for x.

## Logarithmic Functions

The log function is simply the inverse of the the exponential function, it is used to model functions that grow exponentially and also to transform equations.

** **

Also if we have a log of a number the same as the base then it equals 1.

### Logarithmic Laws

There are a few logarithmic laws ,which will help us to perform our algebraic operations.

### Logarithmic Example

For an example lets take an example of question 6 from the 2014 exam one.

Solve:

Our first step is to group the logs onto one side.

## Feedback

Want to suggest an edit? Have some questions? General comments? Let us know how we can make this resource more useful to you.