1. Properties of Logarithms
Section 3.3

2. 3.3 PROPERTIES OF LOGARITHMS
Change of base formula:
loga x = logb x / logb a
= log x / log a
= ln x / ln a
Evaluate log
log / log10 9
log 1043 / log 9
3.1630
Evaluate using ln: log
ln 1043 / ln 9
Same!

3. Properties of Logarithms:
loga (uv) = loga u + loga v
ln (uv) = ln u + ln v
loga u/v = loga u – loga v
ln u/v = ln u – ln v
loga un = n loga u
ln un = n ln u

4. Write each log in terms of ln 2 & ln 3:

5. Verify that – log10 1/100 = log10 100
-log =
-(-1) log =
log =
Expand each expression:
log4 5x3y
log4 5 + log4 x3 + log4 y
log log4 x + log4 y

6. ln √3x – 5 7
ln (3x-5)1/2
ln (3x – 5)1/2 – ln 7
½ ln (3x – 5) – ln 7
Condense each expression:
½ log10 x + 3 log10 (x + 1)
log x1/2 + log (x + 1)3
log [ √ x (x + 1)3]

7. 2 ln (x + 2) – ln x
ln (x + 2)2 – ln x
ln (x + 2)2 2
1/3 [log2 x + log2 (x – 4)]
1/3 {log2 [x(x – 4)]}
log2 [x(x – 4)]1/3
log2 3√ x(x – 4)

8. Homework
Page
10-20 even, 35, odd, 72, 74