1. ## Logarithm Word Problem?

Having trouble figuring this out, any help? The decibel level of a sound is given by the equation where I is the sound's intensity and I0 corresponds to the intensity of the weakest sound that can be detected by the human ear. A sound of 140 decibels produces pain in the average human ear. Approximately how many times greater than I0 must the intensity I of a sound be to reach this decibel level?
Thanks!

2. ## Re: Logarithm Word Problem?

Let $D=140$, just as the problem says. Then solve for $I$ in terms of $I_0$.

3. ## Re: Logarithm Word Problem?

Originally Posted by SlipEternal
Let $D=140$, just as the problem says. Then solve for $I$ in terms of $I_0$.
Then would I have to be 10^14 times the amount of I0?

4. ## Re: Logarithm Word Problem?

Hello, canyouhelp!

Then would I have to be 10^14 times the amount of Io?

Yes!

. . 10 log10(I/Io) .= .140

. . . . log10(I/Io) .= .14

. . . . . . . . .I/Io .= .1014

. . . . . . . . . . .I .= .1014 Io

5. ## Re: Logarithm Word Problem?

Originally Posted by canyouhelp
Then would I have to be 10^14 times the amount of I0?
Correct!

Thanks guys!