SECT 2.3LOGARITHM RULES
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RULE #1
Challenge: Solve for “x”
If the “Base” and the“Number” have the value
Then the “Exponent” and the“Logarithm” will be equal
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RULE #2 “POWER LAW”
Proof:
Multiply bothsides by “n”
Take bothsides to the
Power of “n”
“If an exponent appears in the logarithm,you can move it to the front of the logarithm
and multiply them”
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RULE #2B POWER LAW CONTINUED….
Simplify:
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TIPS FOR SIMPLIFYING LOGARITHMS WITHNUMBERS ONLY
Reduce each number to a power with prime base
This will make the logarithms easier to cancel eachother out
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EX: SIMPLIFY EACH OF THE FOLLOWINGLOGARITHMS WITHOUT A CALCULATOR:
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RULE #3) MULTIPLICATION LAW
If this value isa product of 2 ormore numbers
Then you can separate it as
the sum of the ”LOG” of each value
Proof:
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RULE #4) DIVISION LAW
If this value isa quotient of 2 ormore numbers
Then you can separate it as
the difference of the ”LOG”each value
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TIPS FOR DIVISION & MULTIPLICATION LAWS
Both laws can be used backwards
The sum or difference of two or more logarithms can becombined together as one log with the terms beingmultiplied or divided
Terms that are added will be in the numerator
Terms that are subtracted will be in the denominator
NOTE: all the Logs must have the SAME base!!
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EX: SIMPLIFY EACH OF THE FOLLOWING TO ASINGLE LOGARITHMIC FUNCTION:
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Challenge: Given thatdetermine in terms of “m” and “n”
Isolate Log(x) and Log (y)
Note: Both logs need to have
the same BASE!!!
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HOMEWORK:
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