1. Laws of Logarithms 5.6

2. Laws of Logarithms O If M and N are positive real numbers and b is a positive number such that b  1, then O 1. log b MN = log b M + log b N O 2. log b = log b M - log b N O 3. log b M = log b N if and only if M = N O 4. log b M k = k  log b M, for any real number k.

3. Laws of Logarithms O 5. O 6. O 7. O 8. *ln has the same laws.

4. Ex. Write each expression in terms of Log M and log N. O A) log O B) O C) log M 2

5. Ex. Write each expression as a rational number or as a single logarithm. O A) ln 2 + ln 6 – ln 9 O B) log 6 9 + log 6 5 O C) log 3 – log 6 – log 5 O D) (2log b M – log b N – log b P)

6. Ex. Simplify each expression with out a calculator. O A) ln e 2 B) ln O C) ln e 3x + 5 D) 10 2 log 6 O E) 10 3 + log 4 F) e 1 + 2 ln x

7. Ex. Solve the given equation. O A) log 2 (x + 2) + log 2 5 = 4 O B) log 4 (2x + 1) – log 4 (x – 2) = 1

8. Ex. Express y in terms of x O O Ex. 6 Given log 4 3 = x & log 4 7 =y, write the following in terms of x and y: O log 4 63