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 Examples Use calculator to evaluate each log to four decimal places ID: 799259
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Slide1
9.4 Common Logarithms
Slide2Common 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
Slide3Examples: Use calculator to evaluate each log to four decimal places
1. log 3 2. log 0.2
3. log 5 4. log
0.5
Slide4Solve 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 = 11.8 + 1.5M. The Chilean earthquake of 1960 measured 8.5 on the Richter scale. How much energy was released?
Slide5Example 6:
Find
the energy released by the 2004 Sumatran earthquake, which measured 9.0 on the Richter scale and led to the tsunami.
Slide6HELPFUL 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!
Slide7Example
3
x
=11 4x=15
Slide8Solving Inequalities
Example 7
5
3y<8y-1
Slide9Example 8
3
2x
>6x+1
Slide10Example 9
4
y
<52y+1
Slide11Change of Base Formula
Slide12Example
Express
in
terms of common logs, and then approximate its value to four decimal places.log425 log
318 log7 5