Download Laws of Logarithms

Section 4-3
Math 150 Lecture Notes
Laws of Logarithms
Laws of Logarithms
Let a be a positive number, with a ≠ 1. Let A, B, and C be any real numbers with A > 0 and B > 0.
1. loga (AB) = logaA + loga B
 A
2. loga   = loga A – loga B
B
3. loga (AC) = C loga A
Change of Base Formula
log a x
log b x =
log a b
Example 1: Evaluate the expression. log3 100 – log3 18 – log3 50
Example 2:
Use the Laws of Logarithms to expand the expression:
Example 3: Use the Laws of Logarithms to expand the expression:
1
 a2 

log 4
b c 
ln
3x 2
( x + 1)10
Section 4-3
Example 4: Use the Laws of Logarithms to combine (condense) the expression:
log5 (x2 – 1) – log5 (x – 1)
Example 5: Use the Laws of Logarithms to combine (condense) the expression:
1
1
log(2 x + 1) + [log( x − 4) − log( x 4 − x 2 − 1)]
3
2
Example 6: Use the Change of Base Formula and a calculator to evaluate the logarithm, correct to
four decimal places.
log6 92
2