1. Ch. 3 – Exponential and Logarithmic Functions
3.3 – Properties of Logarithms

2. Properties of Logarithms
3 basic properties:
loga x + loga y = loga (xy)
loga x – loga y = loga (x/y)
loga xy = y loga x
Ex: Condense each logarithmic expression.
Condense doesn’t mean evaluate!
log 8 + log 12 – log 3
log (8•12/3) = log (32)
2 ln(x + 2) – ln x

3. Change of Base Ex: Evaluate log4 29.
Set it equal to x, then scoop the loop!
4x = 29
log 4x = log 29
x log 4 = log 29
x = (log 29)/(log 4)
x = 2.429
To evaluate non-base-10 logs on your calculator, use the change of base formula:

4. Expand completely: log4 5x3y
3 log4 5x + log4 y
log4 5y + 3 log4 x
log4 5 + log4 x3 + log4 y
log log4 x + log4 y
log4 5 • 3 log4 x • log4 y

5. Expand completely: 2 ln(4x + 1) + 2 ln x ½ ln(4x + 1) – 2 ln x

6. Condense completely:

7. Evaluate: log6 .01
-2.570
-1.285
-.333
2.570
1.285