Laws of Logarithms 5.6. Laws of Logarithms O If M and N are positive real numbers and b is a...
8
Laws of Logarithms 5.6
-
Upload
alexandra-kelly -
Category
Documents
-
view
213 -
download
1
Transcript of Laws of Logarithms 5.6. Laws of Logarithms O If M and N are positive real numbers and b is a...
Laws of Logarithms
5.6
Laws of LogarithmsO If M and N are positive real numbers and
b is a positive number such that b 1, then
O 1. logb MN = logb M + logb N
O 2. logb = logb M - logb N
O 3. logb M = logb N if and only if M = N
O 4. logb Mk = k logb M, for any real number k.
Laws of Logarithms
O 5.
O 6.
O 7.
O 8. *ln has the same laws.
Ex. Write each expression in terms of Log M and log N.
O A) log
O B)
O C) log M2
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)
Ex. Simplify each expression with out a calculator.
O A) ln e2
B) ln
O C) ln e3x + 5
D) 102 log
6
O E) 103 + log 4
F) e1 + 2 ln
x
Ex. Solve the given equation.
OA) log 2 (x + 2) + log 2 5 = 4
OB) log 4 (2x + 1) – log 4 (x – 2) = 1
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
