Download Topic: Laws of Logs

N9-45
Topic: Laws of Logs
If M and N are positive real numbers and b is a positive
number other than 1, then
1. logbMN = logbM + logbN
2. logb M = logbM - logbN
N
3. logbM = logbN if and only if M = N
4. logbMk = k logbM for any real number k.
5. change-of-base formula: logbc =
Exponents
VS.
log c
log b
Logarithms
x 2  x3 
log xy =
x5

2
x
log
 2
 x 


5
=
x
=
y
log x 2 
Express in terms of log M and log N.
1. log M2
N
2.
logMN 2
Express as a single logarithm or rational number.
3. log2 48 - 1 log2 27
3
4. 1 (logbM + logbN - logbP)
2
Simplify:
5. ln e4
6. 10log6
Express y in terms of x.
7.
log y + 1 log x = log 3
2
Use the change-of-base formula to find the value of the logarithm.
Round to 3 decimal places.
8. log29 =
9. log46 =