1. 7.5 – Properties of Logarithms
Expanding Logs

2. Laws of Logarithms 1. logb MN = logb M + logb N
If M and N are positive real numbers
and b is a positive number such that b  1, then
1. logb MN = logb M + logb N
2. logb = logb M - logb N
3. logb Mk = k  logb M, for any real number k.

3. Order for Expanding:
1. Quotient
2. Product
3. Power

4. Ex. Expand in terms of log M and log N.
B) 𝑙𝑜𝑔 3 𝑀 𝑁

5. Ex. Expand in terms of log M and log N.
𝑙𝑜𝑔 𝑀 2 𝑁
𝑙𝑜𝑔 4 4 𝑥 3 𝑦

6. Ex. Expand (You try)
a. 𝑙𝑜𝑔 5 𝑀 𝑁 3
b. 𝑙𝑜𝑔 𝑀𝑃 𝑁 3

7. 7.5 – Properties of Logarithms
Condensing Logs

8. Order for Condensing:
1. Power
2. Product
3. Quotient

9. Ex. Write each expression as a rational number or as a single logarithm. (Condense)
A) ln x + ln y – ln z
B) 𝑙𝑜𝑔 6 (𝑥−2)+ 𝑙𝑜𝑔 6 (𝑥+5)

10. Ex. Write each expression as a rational number or as a single logarithm. (Condense)
C) log a – log b – log c
D) 𝑙𝑜𝑔 𝑏 𝑀− 𝑙𝑜𝑔 𝑏 𝑁+ 𝑙𝑜𝑔 𝑏 𝑃

11. Ex. Condense (You try)
a. log 𝑀 +5 log 𝑁− 1 2 log 𝑃 b. 1 2 𝑙𝑜𝑔

12. Ex. Condense (You try)
c. 2 𝑙𝑜𝑔 3 𝑥− 𝑙𝑜𝑔 3 𝑦

13. Ticket Out:
Expand: log 𝑥 3 𝑦 4 𝑧 Condense: 2 log 𝑥 +3 log 𝑦 log 𝑧