1. 3.4 Properties of Logarithmic Functions

2. Properties of Logarithms
Product Rule: logb(RS) = logbR + logbS
Ex) ln 8x =
Quotient Rule: logb(R/S) = logbR – logbS
Ex) log (3/x) =
Power Rule: logbRc = c logbR
Ex) log2x-2 =

3. You Try. Write the expression as a sum or difference of logarithms
You Try! Write the expression as a sum or difference of logarithms or multiples of logarithms
ln 9y
log2y5
ln (x2/y3)

4. You Try! Write the expression as a single logarithm
log5x + log5y
2 ln x + 3 ln y
4 log (xy) – 3log (yz)

5. Change-of-Base Formula
For positive real numbers a, b, and x with a ≠1 and b ≠1, or

6. Use the change-of-base formula and your calculator to evaluate the logarithm:
You Try!
Log8175
Log0.512

7. Graphing Logarithmic functions
If b > 1, the graph of g(x) = logbx is a vertical stretch or shrink of the graph of ln (x) by the factor of 1/ ln b.
If 0 < b < 1, a reflection across the x-axis is required as well.

8. Describe how to transform the graph of f(x) = ln x into the graph of the given function:
g(x) = log5x

9. Describe how to transform the graph of f(x) = ln x into the graph of the given function:
h(x) = log1/4x

10. f(x) = ln (x3) Domain Range Continuity Increasing Decreasing
Asymptotes
End Behavior

11. Homework
Pg. 317 (4, 6, 12, 20, 22, 28, 40, 42, 49)