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Math Help - Logarithm Word Problem?

  1. #1
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    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?
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  2. #2
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    Re: Logarithm Word Problem?

    Let $D=140$, just as the problem says. Then solve for $I$ in terms of $I_0$.
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    Re: Logarithm Word Problem?

    Quote Originally Posted by SlipEternal View Post
    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?
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  4. #4
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    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
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  5. #5
    MHF Contributor ebaines's Avatar
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    Re: Logarithm Word Problem?

    Quote Originally Posted by canyouhelp View Post
    Then would I have to be 10^14 times the amount of I0?
    Correct!
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    Re: Logarithm Word Problem?

    Thanks guys!
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