The sound intensity of a typical vacuum cleaner is 80 dB (decibels). Sound intensity of 160 dB will burst an eardrum. How many times louder is the sound that will burst an eardrum than the sound of a vacuum cleaner?

-Four hundred times as loud.
-Ten thousand times as loud.
-Forty thousand times as loud.

Question

The sound intensity of a typical vacuum cleaner is 80 dB (decibels). Sound intensity of 160 dB will burst an eardrum. How many times louder is the sound that will burst an eardrum than the sound of a vacuum cleaner?

-Four hundred times as loud.
-Ten thousand times as loud.
-Forty thousand times as loud.

anonymous · Answer

I'm supposed to use logarithms to solve it.

phi · Answer

did they give you a definition of decibels ?

anonymous · Answer

no

phi · Answer

the difference between 90 dB and 180 dB is 90 dB

use
$$ 20 \log_{10} x = 80 \ dB $$
and solve for the factor x

phi · Answer

I would start by dividing both sides by 20

anonymous · Answer

x=10,000 @phi

phi · Answer

log x = 4
x = 10^4
or 
x= 10000
yes