1. Properties Continued

2. #5 – Product Law: logaxy = logax + logay
When adding two or more log expressions with the same base, combine them and multiply the arguments to form a new single log

3. log22 + log25 = x log2(2x5) = log210 = x log10 = x log2 3.32 = x
Example
log22 + log25 = x log2(2x5) = log210 = x log10 = x log = x

4. #6 – Quotient Law: logc(m/n) = logcm - logcn
When subtracting two log expressions with the same base, combine them and divide the arguments to form a new single log. ORDER MATTERS!

5. log333 - log311 = x log3(33/11) = x log33 = x x = 1 (by property #2)
Example
log333 - log311 = x log3(33/11) = x log33 = x x = 1 (by property #2)

6. Example
log296 - log23 = x log2(96/3) = x log232 = x 2x = 32 x = 5 (mentally or with calculator)

7. Example
log2(8/3) = log28 - log23 = 3 - log23 (since log28=3) = 3 – 1.58 (since log23=1.58) = 1.42

8. #7 –Law of Powers: logcxn = nlogcx
When the argument has an exponent, that numbers because a coefficient to the log expression (and loses the exponent)

9. log243 3log24 3(2) (since log24=2) So log243= 6
Example
log243 3log24 3(2) (since log24=2) So log243= 6

10. Example
3log46 = log263

11. Example
log2 3√7 = log27⅓ = ⅓log27 = ⅓(2.81) = 0.94

12. log7493 = 3log749 = 3(2) (since log749=2) = 6
Example
log7493 = 3log749 = 3(2) (since log749=2) = 6

13. #8 – Change of Base Law: logcx = logx (we already know this one!) logc
This is how we calculate logs on a calculator! (Remember we can use ln too!)

14. Example
log57 = x x = (log7/log5) x = 1.2

15. Example
7x = 400 log7400 = x x = log400 log7 x = 3.07

16. HOMEWORK
Workbook p.176 #7, 8 p. 177 #9, 12, 14 p. 179 #21, 25, 26 ***QUIZ on Monday on Exponents and Logs (open book!!) GO TO RECUP TOMORROW IF YOU NEED HELP!!!!!