Reflection

This week in calculus, we worked with solving natural logarithms by using different methods like solving for derivatives.
Section 5.1
EXAMPLES
Expand.
1) ln xy^2/5
lnx + lny^2 – ln5
= lnx + 2lny – ln 5

Condense.
2) 2ln(x+3) – ln(x-4)
= ln (x+3)^2/(x-4)

Use ln3 ~ .49 and ln4 ~ .23 to approximate ln12
3) ln4/3 = ln4 – ln3
= .23 - .49
= -.26

Section 5.4
To solve for a variable when it’s an exponent:
1. Take the ln of both sides.
2. Bring the variable to the front of the ln.
To solve for a variable if it’s inside a log:
1. Rewrite as an exponent.
2. Solve for x.

EXAMPLES
1) 6 = e^x-2
ln6 = lne^x-2
ln6 = x-2
x = ln6-2

2) ln(3x-2) = 9
e^9 = 3x-2
e^9+2 = 3x
x = e^9+2/3

3) e^x = 12
lne^x = ln12
x = ln12
~ 2.485