1. 8.3 – Logarithmic Functions and Inverses

2. What is a logarithm?
A logarithm is the power to which a number must be raised in order to get some other number
For example, the base ten logarithm of 100 is 2, because ten raised to the power of two is 100:
100 = 102 because log = 2

3. Convert

4. Remember: If y = bx then logby = x
Ex: Write the following equations in logarithmic form
Remember: If y = bx then logby = x
If 25 = 52
then
Log525=2
If 729 = 36
then
Log3729=6
If 1 = 100
then
Log101=0 If
then

5. Let’s try some: Converting between the two forms.
Expo Form Log Form

6. Common Logs
A common log is a logarithm that uses base 10. You can write the common logarithm log10y as log y (they are the logs you use on your calculator, with no base shown it = 10)
Scientists use common logarithms to measure acidity, which increases as the concentration of hydrogen ions in a substance. The pH of a substance equals

7. Evaluating Logarithms
Ex: Evaluate log816
Log816=x Write an equation in log form
16 = 8x Convert to exponential form
24 = (23)x Rewrite using the same base. In this case, base of 2
24 = 23x Power of exponents
4 = 3x Set the exponents equal to each other
x=4/ Solve for x
Therefore, Log816=4/3

8. Evaluating Logarithms
Ex: Evaluate
Write an equation in log form
Convert to exponential form
Rewrite using the same base. In this case, base of 2. Use negative expos!
-5 = 6x Set the exponents equal to each other
x=-5/ Solve for x
Therefore,

9. Let’s try some
Evaluate the following: