1. 8.6 Natural Logarithms

2. Natural Logs and “e” Or what we commonly refer to it as is y = ln x
Or what we commonly refer to it as is y = ln x
“e” is Euler’s number. e ≈
It is also used for compound interest

3. All the rules still apply
You can use your product, power and quotient rules for natural logs just like you do for regular logs. Also you cannot have a negative inside the log.
Let’s try one:

4. Solving with base “e” x = 0.458 1. Subtract 2.5 from both sides
2. Divide both sides by 7
3. Take the natural log of both sides.
4. Simplify.
5. Divide both sides by 2
x = 0.458
6. Calculator

5. Another Example: Solving with base “e”
1. Take the natural log of both sides.
2. Simplify.
3. Subtract 1 from both sides
x = 2.401
4. Calculator

6. Solving a natural log problem
To “undo” a natural log, we use “e”
1. Rewrite in exponential form
2. Use a calculator
3. Simplify.

7. Another Example: Solving a natural log problem
1. Rewrite in exponential form.
2. Calculator.
3. Take the square root of each time
3x+5 = 7.39 or -7.39
4. Calculator
X=0.797 or
5. Simplify

8. Let’s try some