Amy's Reflection #6

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

(remeber b-rob might use random symbol so don't panic)

ok i know i just explained logarithms but im nervous about monday's test...i really don't like the word problems on the chapter test on page 209...if anyone one can explain an easy way to solve them i'll be really greatfull...