1. 9.4 Common Logarithms

2. Logarithms with base 10 are common logs
Common Logarithms
Logarithms with base 10 are common logs
You do not need to write the 10 it is understood
Button on calculator for common logs
LOG

3. Examples: Use calculator to evaluate each log to four decimal places
1. log log 0.2
3. log log 0.5

4. Solve Logarithmic Equations
Example 5:
The amount of energy E, in ergs, that an earthquake releases is related to is Richter scale magnitude M by the equation logE = M. The Chilean earthquake of 1960 measured 8.5 on the Richter scale. How much energy was released?

5. Example 6:
Find the energy released by the 2004 Sumatran earthquake, which measured 9.0 on the Richter scale and led to the tsunami.

6. HELPFUL HINT
If both sides of the equation cannot be easily written as powers of the same base you can solve by taking the log of each side!

7. Example
3x= x=15

8. Solving Inequalities
Example 7
53y<8y-1

9. Example 8
32x>6x+1

10. Example 9
4y<52y+1

11. Change of Base Formula

12. Example
Express in terms of common logs, and then approximate its value to four decimal places.
log425 log log7 5