1. Warm Up – 4/23 - Thursday
Erin deposits $1200 into a bank account that grows
at an interest rate of 5%. Find the amount in the account
after 3 years if the interest is compounded:
A) Annually B) Monthly C) Continuously
2. Bill has had his money in a savings account for 10 years.
The account currently has $2, If the account
accumulates interest at a rate of 3% compounded
quarterly, find how much Bill initially deposited.

2. Quiz Friday Sketching Exponential Functions
Compound Interest/Compounding Continuously
Converting an Exponential to a Log
Converting a Log to an exponential

3. Properties of Logs CW

4. Rules of Logarithms log 𝑎 𝑏 + log 𝑎 𝑐 = log 𝑎 (𝑏∙𝑐)
THESE RULES ONLY APPLY IF THE BASE IS THE SAME!!!
log 𝑎 𝑏 + log 𝑎 𝑐 = log 𝑎 (𝑏∙𝑐)
log 𝑎 𝑏 − log 𝑎 𝑐 = log 𝑎 𝑏 𝑐
log 𝑎 𝑏 𝑐 =𝑐∙ log 𝑎 𝑏

5. Example #1
log log 3 4

6. Example #1 - Solution
When I add logs with the same base, I can multiply their insides.
log log 3 4
= log 3 5∙4 = log 3 (20)

7. Example #2
log log log 7 5

8. Example #2 - Solution log 7 4 + log 7 2 + log 7 5

9. Example #3
log − log 8 4

10. Example #3 - Solution When we subtract logs, we divide the insides.
log − log 8 4
log , If possible reduce the fraction, if not leave it as is.

11. Example #4
log 7 − log log 2

12. Example #4 - Solution
Whenever mixing addition and subtraction, work from left to right.
log 7 − log log 2
log log 2
log ∙2 = log

13. Example #5
2log 9 7

14. Example #5 - Solution
When we multiply on the outside of the log we can move that number into the exponent on the inside!
2 log = log = log

15. Example #6
3 log −2 log 3 (2)

16. Example #6 - Solution We ALWAYS take care of the exponents first!
3 log −2 log 3 (2)
log − log
log − log 3 4
log