1. Algebra 2
Warmup

2. 9.2 Logarithms Start with an exponential function: y = bx
When you flip that function over the y = x line, the function becomes x = by
This is what we call the inverse.
Given y = bx, y is
called the logarithm of x
y = logbx

3. Recap The logarithm of x with base b looks like this... y =logbx
It is defined as the exponent y that makes the equation x = by true.
So basically...y = logbx can be rewritten as
x = by....they are the same just in different forms.

4. Example 1 Write each equation in exponential form.
Remember: y = logbx x = by

5. Example 2 Write each equation in logarithmic form.
Remember: x = by y = logbx

6. Example 3 Set the expression equal to y Rewrite in exponential form
Evaluate the logarithmic expression
Set the expression equal to y
Rewrite in exponential form
Write 64 with base of 2
Set exponents equal
Solve
Your Turn

7. Characteristics of a Logarithmic Function
Function is continuous and one-to-one
Domain is all positive real numbers
Y-axis is an asymptote of the graph
Range is all real numbers
Graph contains the point (1,0)...x-intercept is 1.

8. Example 4
Evaluate each expression b) c) a) d)
Notice a short cut?

9. Logarithmic Equation Equation that contains one or more logarithms.
Example 5a & b: Solve the following equations.
Remember: logbx = y x = by

10. Property of Equality for Logarithmic Functions
If b is a positive number other than 1, then logbx = logby if and only if x = y.
Example: If log7x = log73, then x = 3
The log bases must be equal!!

11. Logarithmic Inequality
Change from logarithmic to exponential inequality
(x can not be smaller than 0)

12. Solving log equations – Example 6
Extraneous solutions: Recall that the domain of a log function is all POSITIVE #’s...therefore you need to check solutions!
CHECK!!
Is undefined...solution is extraneous

13. Your turn – Example 7 CHECK!!
Solve the equation and check your solution(s).
CHECK!!

14. Homework Assignment #57
p all, odd