1. 4.2 Logarithms

2. b must always be greater than 0 y is the exponent X is the argument
b is the base
b CANNOT = 1
b must always be greater than 0
y is the exponent
can be all real numbers
X is the argument
must be > 0
“logbx is the exponent to which the base b must be raised to give you x.”

3. Write in the other form:
32 = 9
log 6216 = 3

4. Properties
loga1 = 0
logaa = 1
logaax = x

5. Evaluate:
log10100,000 log164 log51 log558

6. Solve for the variable.
logb9 = 2

7. Log functions and exponential functions are inverses of each other.
Since the domain of an exponential is all real numbers and the range is y > 0, then for:

8. Graph: y = log2x

9. Explain the graphs of: y = -log2x y = log2(-x)
Reflect across the x-axis
Reflect across the y-axis

10. y = -log2x
y = log2(-x)

11. Common Logarithms – base 10
logx = log10x
Natural Logarithms – base e
lnx = logex
y = lnx is the inverse of y = ex

12. Simplify
log 4 log 0.1
ln 1 ln e
ln e8 ln 5

13. Explain the graphs and find the domain.
y = 2 + log5x
y = log10(x – 3)
y = ln (4 – x2)
Shift vertically up 2
Shift horizontally right 3

14. Homework pg 349 #3-37 odd, all