8.6 Natural Logarithms

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 ≈ 2.71828 It is also used for compound interest

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:

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

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

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

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 -4.130 5. Simplify

Let’s try some