5-6

Mardi Gras Break Blog #2:
5-6
Properties of Logs:
1. Log b MN = log b M + log b N
2. Log b M/N = log b M – log b N
3. Log b M^k = k log b M
(RIGHT SIDE IS CONDENSED, LEFT SIDE IS EXPANDED).

EXAMPLE 1: Condense log M – 3 log N
A). First, check to see which property it’s following. With the – sign, we automatically know the
answer will be in fraction form, property #2.
B). Also, the second half (3 log N) is property #3. Changing that, we get log N^3
C). Now we can continue..
log M/log N^3

EXAMPLE 2: Condense log 8 + log 5 – log 4
A). Simply the 3 parts to get 2 so we can condense. Since log 8 and log 5 are the same, multiply 8 and 5.
B). Now we have log 40 – log 4.
C). Having the – sign, we know we’re going to follow property #2.
log 40/log 4
D). Your answer is 10.

EXAMPLE 3: Expand log b MN^2
A). Following property #1, we get log b M + log b N^2
B). Now bring all exponents to the front to get your final answer.
log b M + 2 log b N