# Converting Between Logarithmic and Exponential Functions

How to Convert Between Logarithmic and Exponential Functions -
You already know that the log and exponential functions are inversely proportional to each other. However, what will you do if some tell you to convert a log function to an exponential one or vice versa? We will discuss this here in detail
First, you should be aware of how each function is written. The log function is written in the form of y= log_{b}x, while the same function in the exponential form is written in the form of b^{y} = x. Now, to learn conversion from an exponential form to the logarithm form, let us consider an example.
5^{x} = 25. In the above equation, the base is the number on the left-hand side of the above function. In the logarithm function, the base lies with the log function. Let's take the above example and rewrite it as a logarithmic function.
x = log_{5}25. Similar is the case when you want to convert a log function to an exponential one. This is a series of lessons and worksheets that help students convert between logarithmic and exponential forms of functions.

### Aligned Standard: HSF-BF.B.5

- Notation Conversions Step-by-step Lesson - A simple restatement of the problem layout works here for us.
- Guided Lesson - We jump back and forth between logs and exponential forms.
- Guided Lesson Explanation - It is all about number sentence structure is what I hear often on this skill.
- Practice Worksheet - Some need logs and some don't! See what works out best for you.
- Matching Worksheet - When you take the format into consideration, these are really multiplication problems.

- Answer Keys - These are for all the unlocked materials above.

### Homework Sheets

Time to switch between the two formats of functions.

- Homework 1 - Remember that the logarithm is the exponent.
- Homework 2 - As the logarithm is the exponent: log
_{b}x = y is x = b^{y} - Homework 3 - This is really just a rearrangement of the values.

### Practice Worksheets

The first two sheets are very manageable. The third sheet is much tougher.

- Practice 1 - Express logarithmic form in exponential form: log
_{2}1024 = 10 - Practice 2 - Express exponential forms in logarithmic form: 6
^{6}= 46656 - Practice 3 - A little more advanced problems here.

### Math Skill Quizzes

They are all about moving from exponential forms to logarithmic forms.

- Quiz 1 - It is all about isolating the exponent.
- Quiz 2 - This is where you can make the right placement and that is all that is needed.
- Quiz 3 - This is a solid ending quiz to see if you understand all the concepts.