Learning Goal: To learn the properties of logarithms and how to manipulate them when solving sound problems. The intensity of sound is the power of the sound waves divided by the area on which they are incident. Intensity is measured in watts per square meter, or W/m² The human ear can detect a remarkable range of sound intensities. The quietest sound that we can hear has an intensity of 10-12 W/m², and we begin to feel pain when the intensity reaches 1 W/m² Since the intensities that matter to people in everyday life cover a range of 12 orders of magnitude, intensities are usually converted to a logarithmic scale called the sound intensity level 3, which is measured in decibels (dB). For a given sound intensity I. B is found from the equation B = (10 dB) log (1) The logarithm of x, written log(x), tells you the power to which you would raise 10 to get a. So, if y = log(x), then a = 10%. It is easy to take the logarithm of a number such as 10². because you can directly see what power 10 is raised to. That is, log(10²) = 2. Part A What is the value of log (1,000,000)? Express your answer as an integer. ▸ View Available Hint(s) log(1,000,000) = ΠΗΓΙ ΑΣΦ Review ?

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Item 9
Learning Goal:
To learn the properties of logarithms and how to manipulate them when
solving sound problems.
The intensity of sound is the power of the sound waves divided by the area
on which they are incident. Intensity is measured in watts per square meter,
or W/m².
The human ear can detect a remarkable range of sound intensities. The
quietest sound that we can hear has an intensity of 10-¹2 W/m², and we
begin to feel pain when the intensity reaches 1 W/m². Since the
intensities that matter to people in everyday life cover a range of 12 orders
of magnitude, intensities are usually converted to a logarithmic scale called
the sound intensity level 3, which is measured in decibels (dB). For a given
sound intensity I, B is found from the equation
ß = (10 dB) log (1).
where Io = 1.0 × 10-¹2 W/m².
Part A
What is the value of log(1,000,000)?
Express your answer as an integer.
► View Available Hint(s)
The logarithm of x, written log(x), tells you the power to which you would raise 10 to get x. So, if y = log(x), then x = 10%. It is easy to take the logarithm of a number such as 10²,
because you can directly see what power 10 is raised to. That is, log(10²) = 2.
log (1,000,000)
=
OF
ΠΙ ΑΣΦ
200
<
?
9 of 15 >
Review
Transcribed Image Text:Item 9 Learning Goal: To learn the properties of logarithms and how to manipulate them when solving sound problems. The intensity of sound is the power of the sound waves divided by the area on which they are incident. Intensity is measured in watts per square meter, or W/m². The human ear can detect a remarkable range of sound intensities. The quietest sound that we can hear has an intensity of 10-¹2 W/m², and we begin to feel pain when the intensity reaches 1 W/m². Since the intensities that matter to people in everyday life cover a range of 12 orders of magnitude, intensities are usually converted to a logarithmic scale called the sound intensity level 3, which is measured in decibels (dB). For a given sound intensity I, B is found from the equation ß = (10 dB) log (1). where Io = 1.0 × 10-¹2 W/m². Part A What is the value of log(1,000,000)? Express your answer as an integer. ► View Available Hint(s) The logarithm of x, written log(x), tells you the power to which you would raise 10 to get x. So, if y = log(x), then x = 10%. It is easy to take the logarithm of a number such as 10², because you can directly see what power 10 is raised to. That is, log(10²) = 2. log (1,000,000) = OF ΠΙ ΑΣΦ 200 < ? 9 of 15 > Review
Expert Solution
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The logarithm of x written log(x) tells you the power to which you would raise 10 to get a So, if y = log(x) then x = 10^y. It is easy to take the logarithm of a number such as 10² because you can directly see what power 10 is raised to. That is, log(10²) = 2

We're required to calculate log(1,000,000). 

 

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