Results 1 to 8 of 8

Math Help - Logarithmic and Exponential functions

  1. #1
    Member
    Joined
    Jun 2012
    From
    Australia
    Posts
    86

    Logarithmic and Exponential functions

    Hello,

    Not sure if this is in the right forum - feel free to move it.

    I have a question from my textbook that is throwing me off a bit.

    The relative loudness of a sound D of intensity I is measured in decibels (db) where

    D = 10 log I/Io

    and Io is the standard threshold of audibility.

    A) Express the intensity of I of a 30-db sound (the sound level of normal conversation) in terms of Io.

    I think I'm supposed to form an equation for I in relation to Io, but I'm not sure what I'm supposed to do. Apparently the answer is "10^3(Io)".

    I'm thinking it's something to do with the fact that I = 30, and the fact that there's a 10 log expression - something to do with the 3 being a divisor of 30 (by 10). I'm just not sure how the 30 gets turned into the exponent of 10 (expressed as 3).

    Any tips?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,661
    Thanks
    1481

    Re: Logarithmic and Exponential functions

    Quote Originally Posted by astuart View Post
    Hello,

    Not sure if this is in the right forum - feel free to move it.

    I have a question from my textbook that is throwing me off a bit.

    The relative loudness of a sound D of intensity I is measured in decibels (db) where

    D = 10 log I/Io

    and Io is the standard threshold of audibility.

    A) Express the intensity of I of a 30-db sound (the sound level of normal conversation) in terms of Io.

    I think I'm supposed to form an equation for I in relation to Io, but I'm not sure what I'm supposed to do. Apparently the answer is "10^3(Io)".

    I'm thinking it's something to do with the fact that I = 30, and the fact that there's a 10 log expression - something to do with the 3 being a divisor of 30 (by 10). I'm just not sure how the 30 gets turned into the exponent of 10 (expressed as 3).

    Any tips?
    Is this \displaystyle \begin{align*} \frac{10\log{I}}{I_0} \end{align*} or \displaystyle \begin{align*} 10\log{\left(\frac{I}{I_0}\right)} \end{align*}?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Jun 2012
    From
    Australia
    Posts
    86

    Re: Logarithmic and Exponential functions

    Whoops, bit of a difference there. It's 10 log (I/Io)
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,661
    Thanks
    1481

    Re: Logarithmic and Exponential functions

    Quote Originally Posted by astuart View Post
    Whoops, bit of a difference there. It's 10 log (I/Io)
    Is the logarithm base 10 or base e?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Member
    Joined
    Jun 2012
    From
    Australia
    Posts
    86

    Re: Logarithmic and Exponential functions

    It doesn't specify, it's just written in the textbook as I've written above. I'm assuming it's log10, because previous questions have used 'ln' to denote log e.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,661
    Thanks
    1481

    Re: Logarithmic and Exponential functions

    Well then let D = 30 and transpose the equation so that you have \displaystyle \begin{align*} I_0 = \dots \end{align*}
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Newbie
    Joined
    Aug 2012
    From
    India
    Posts
    6

    Re: Logarithmic and Exponential functions

    Quote Originally Posted by astuart View Post
    Hello,

    Not sure if this is in the right forum - feel free to move it.

    I have a question from my textbook that is throwing me off a bit.

    The relative loudness of a sound D of intensity I is measured in decibels (db) where

    D = 10 log I/Io

    and Io is the standard threshold of audibility.

    A) Express the intensity of I of a 30-db sound (the sound level of normal conversation) in terms of Io.

    I think I'm supposed to form an equation for I in relation to Io, but I'm not sure what I'm supposed to do. Apparently the answer is "10^3(Io)".

    I'm thinking it's something to do with the fact that I = 30, and the fact that there's a 10 log expression - something to do with the 3 being a divisor of 30 (by 10). I'm just not sure how the 30 gets turned into the exponent of 10 (expressed as 3).

    Any tips?
    While defining dB the base of logarithm is always 10.

    10 \log(\frac{I}{I_0})=30

    \Rightarrow \log(\frac{I}{I_0})=3

    Hence by definition of log ie. if

    [TEX]10^x=y[\TEX] Then [TEX]\log{(y)}=x [\TEX]

    we get,

    \Rightarrow \frac{I}{I_0}=10^3

    \Rightarrow I=10^3 I_0
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Member
    Joined
    Jun 2012
    From
    Australia
    Posts
    86

    Re: Logarithmic and Exponential functions

    Quote Originally Posted by mundhadashantanu View Post
    While defining dB the base of logarithm is always 10.

    10 \log(\frac{I}{I_0})=30

    \Rightarrow \log(\frac{I}{I_0})=3

    Hence by definition of log ie. if

    [TEX]10^x=y[\TEX] Then [TEX]\log{(y)}=x [\TEX]

    we get,

    \Rightarrow \frac{I}{I_0}=10^3

    \Rightarrow I=10^3 I_0
    Ah, that makes a bit more sense.

    I was getting lost when I got to the point of 3 = log (I/Io). Didn't cross my mind to figure out the inverse.

    If 3 = log (I/Io) then 1000 = (I/Io) = 10^3.

    10^3 = (I/Io)
    10^3(Io) = I

    Cheers guys!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Exponential and Logarithmic Functions
    Posted in the Algebra Forum
    Replies: 2
    Last Post: December 12th 2010, 04:42 PM
  2. exponential & logarithmic functions
    Posted in the Calculators Forum
    Replies: 4
    Last Post: November 27th 2009, 06:59 PM
  3. Exponential and logarithmic Functions help
    Posted in the Algebra Forum
    Replies: 3
    Last Post: May 6th 2009, 04:16 PM
  4. Logarithmic and Exponential Functions?
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 23rd 2008, 02:00 PM
  5. exponential and logarithmic functions
    Posted in the Algebra Forum
    Replies: 2
    Last Post: July 20th 2008, 02:04 PM

Search Tags


/mathhelpforum @mathhelpforum