## Converting Between Logarithmic and Exponential Forms

#### Aligned To Common Core Standard:

**High School Functions** - HSF-LE.A.4

How to Convert Between Logarithmic and Exponential Forms - Logarithmic and exponential forms are an important part of mathematics. Given that, they are the core concepts used behind the calculation of the magnitudes of the earthquakes. For example, you can compare the magnitudes of two earthquakes, by converting between logarithmic and exponential form.
For example, the amount of energy released from the first earthquake was 500 times greater than the energy released from the other. The equation that represents this is the problem is 10^{x} = 500, where x is the difference of magnitude placed on the Richter scale. We have to solve for x.
Now, there are different ways to convert them. The first is by using the graphing method. However, estimating from the graphing method can result in an imprecise answer. Thus, we use a log to convert the above exponential function in a logarithmic function.
Let's find out practically. First, we have to learn the values of b, y, and x, to write the equation in log form. The b is the base for log form, while x and y are the unknown variables of the function. In the present example 10^{x} = 500, The value of b is 2, while the value of x and y are 3 and 8, respectively.
log_{10} 500 = x. You can use these lessons and worksheets to learn how to transfer values between exponential and logarithmic forms.

### Printable Worksheets And Lessons

- Exponential Form Step-by-Step Lesson- Exponential form from logarithmic form. A simple step to get us started.
- Guided Lesson - The basketball court graphic you ask? I once sat in a lecture about how almost all shots taken in college basketball can be predicted all based on crowd noise. Yes, it was a log calculation.
- Guided Lesson Explanation - It is all based on a basic conversion that most people can do with ease.
- Practice Worksheet - Remind students that you can't turn a log into a log or an exponent into an exponent.
- Matching Worksheet - Match the conversion with the sentence that explains it.
- Express Exponential Forms in Logarithmic Form Worksheet Five Pack - Make them log based.
- Express Logarithmic Form in Exponential Forms Worksheet Five Pack - Time to go all exponential; over the place!