Logarithm Properties:
- logb MN = logb M + logb N
- logb M/N = logb M - logb N
- logb M^K = K logb M
- logb b^k = k (this one i don't get..maybe i copied it wrong)
- b^logb^k = k
Here are some examples:
1. log 2 + log 3 + log 4 = log 24 (mulitply: 2 x 3 x 4)
2. log 8 + log 5 - log 4 = log 10 (mulitply: 8 x 5 then divide: 40/4)
3. 2 ln 6 - ln 3 = ln 12 (raise 6 to the 2nd power = 36 the divided by 3 = 12)
4. log M - 3 log N = log M/ N^3
5. ln 2 + ln 6 - 1/2 ln 9 = ln 12/3 = ln 4
6. Expand logb MN^2....logb M + 2 logb N
7. Condense log 45 - 2 log 3....log (45/9) = log 5
8. Rewrite in exponetial form: log36 6 = 1/2....36^1/2 = 6
9. Rewrite in logarithmic form: 2^2 = 4....log2 4 = 2
Changing Bases: (Done when you can't solve a log)
- Rewrite it as an exponential
- Take the log of both sides
- Move the variable to the front
- then solve
(use the same steps when solving for x as an exponent when you can't write them as the same base)
examples:
1. log5 10 = x
5^x = 10
log 5^x = log 10
x log 5 = 1
x = 1/log 5
2. 2^x = 7
log 2^x = log 7
x log 2 = log 7
x = log 7/log 2
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