Posted by Soroban on September 10, 2002 at 15:31:19:
In Reply to: decibals and Logarithms posted by Tootsie on September 10, 2002 at 13:56:33:
: The decibel level is obtained from the formula
: D= 10 log10 L
: where L is the loudness of the sound.
: How many times louder is a thunderclap than city traffic noise?
: Thunderclap dB = 120 and loudness = 10^12
: City traffic noise dB = 80 and loudness = 10^8
: Is it really a matter of 10^12 - 10^8 = 10^4?
: Help, help, help.
Tootsie,
"Help, help, help" is appropriate.
You last statement was a teacher's nightmare:
Two incorrect steps --> Correct answer!
How many times larger is 50 than 2?
The answer is NOT 50 - 2 = 48 times larger, obviously.
The answer is 50/2 = 25 times larger.
Your step should have been: 10^12/10^8.
Then using Laws of Exponents: 10^4
You got the right answer by making two appropriate errors:
subtracting instead of dividing, and subtracting illegally.
In some circles, this is called a "Howler" - a mathematical joke
which is circulated around Faculty Lounges.
Consider reducing 16/64 to 1/4 - by cancelling the 6's.