Holiday Reflection #2

For my second holiday blog, i will do somethin a LITTLE more recent than product and quotient rules...Here is a little review on some stuff from the beginning of chapter 5, NATURAL LOGS!

First off, here is how you expand and condense natural logs:

Expand:
ln xy^2/5
lnx + lny^2 – ln5
= lnx + 2lny – ln 5

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


Some notes to remember when fooling with logarithms:
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.

And here are some examples of this:

6 = e^x-2
ln6 = lne^x-2
ln6 = x-2
x = ln6-2

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

e^x = 12
lne^x = ln12
x = ln12
= 2.485