## The Inverse Relationship of Logarithms and Exponents

#### Aligned To Common Core Standard:

**Building Functions** - HSF-BF.B.5

What is the Inverse Relationship of Logarithms and Exponents?
Logarithms and exponential functions hold an important place in the concept of mathematics. They have an inverse relationship with each other. Let us discuss this in detail.
Firstly, the Exponential Function is written as f(x)=e^{x}, where the value of e is 2.718. This function is used when the value of x is fairly complicated. On the other hand, logarithm in a relationship with the exponential function is called the natural log. The natural log (ln) is the inverse function of the exponential function. In other words, the graph of ln is a reflection across the line with the exponential function's graph.
A series of worksheets and lessons that show students how logs undo exponentials and the relationship that exists between those two.

### Printable Worksheets And Lessons

- Sneaker Company Growth
Step-by-step Lesson- The shoe company wants to grow six times
their current profit. How long will it take?

- Guided Lesson
- How long will it take to pay off the mortgage and "Hello!"
Richter scale.

- Guided Lesson Explanation
- The Richter scale problem will give many students some trouble.

- Practice Worksheet
- We stay on the same themes: paying loans back and fixed growth
scales.

- Matching Worksheet
- I might have forgot a dollar sign or two to make the problems
not so obvious.

#### Homework Sheets

In some cases, the companies presented have an outrageous profit growth. They actually were modelled after real companies.

- Homework 1 - The profit growth of a tea company is 8% every 2 years. If the company were to stay on that track, how long would it take for the company to grow to 5 times its current profit?
- Homework 2 - Find the monthly payments on a $200,000, 23-year mortgage, with monthly payments at 12%. How much interest will you pay over the 23 years?
- Homework 3 - Early in the century, an earthquake with the magnitude of 4 struck in the USA. During the same year, Japan recorded an earthquake that was three times greater. What was the magnitude of the earthquake in Japan?

#### Practice Worksheets

Hello, Richter scale!

- Practice 1 - The Richter scale is used to measure the intensity of Earthquakes. He Richter scale is based on the equation: R= log (I÷I0)
- Practice 2 - Go over the three fundamental methods that apply to these.
- Practice 3 - An earthquake with the magnitude of 5 struck in Russia. During the same year, Africa recorded an earthquake that was three times greater. What was the magnitude of the earthquake in Africa?

#### Math Skill Quizzes

We mix the two skills together here.