NaturalLog.md (905B)
1 # Natural Log 2 3 **Definition:** The natural log (ln) is an expression stating the output of the logarithm function is the value such that e^x is equal to the value being taken as the input. 4 5 When working with ln we have the following options for algebraic manipulations: 6 7 1. Division becomes subtraction 8 - ln(x/y) -> ln(x) - ln(y) 9 2. Multiplication become addition 10 - ln(xy) -> ln(x) + ln(y) 11 3. Exponents can be pulled out 12 - ln(x^2) -> 2ln(x) 13 14 There are no other rules for manipulations so there are times when we are limited in our reduction of equations such as when we are adding together values in the logarithm as this will then not allow us to pull out any of our exponents. 15 16 d/dx ln(|x|) = 1/x 17 18 The |x| is only neccesary for functions that cross into the negative x values. 19 20 ### Chain Rule 21 22 We can also use the chain rule for ln. 23 24 Example: 25 26 $\frac{d}{dx} (ln(g(x))) = \frac{1}{g(x)} \cdot g'(x)$