SOLUTION: To measure the volume of loudness of a sound, the decibel scale is used. The loudness L in decibels (db) of the sound is given by: L =10 log I/I0 where I is the intensity of the so

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Question 251335: To measure the volume of loudness of a sound, the decibel scale is used. The loudness L in decibels (db) of the sound is given by: L =10 log I/I0 where I is the intensity of the sound.
Solve: The band Strange Folk performed in Burlington VT and reached sound levels of 111 db. What is the intensity of the sounds? This is my answer, but my teacher says I did it wrong. Here's what he wrote:
You have made some errors on this question.
--------------------------
L =10 log I/I0
111 = 10 log (l/10)
--------------------------
should be
L =10 log I/I0
111 = 10 log (l/10^(-12)
11.1=log I - log 10^ (-12)
Now solve for I
Thanks!
Answer by jsmallt9(3758)   (Show Source): You can put this solution on YOUR website!
It took me a while to understand what was going on. The equation is

Those are i's in the logarithm, not 1's. And the zero in the logarithm is a subscript, not the digit of a number. I think this is where you got confused. (I know this is where I got confused when I first looked at the problem.)

Since , your teacher's solution:



is correct so far.

And, as your teacher says, we still need to solve for I. Solving for I means we have to get an equation we I is by itself on one side.

We can start by finding the / If we understand logarithms we will know that this must be -12. If you don't see this:
Our equation is now:

or

Next we can subtract 12 from each side:

If you know how to do inverse logarithms on your calculator you can find "I" now. If not, then we can rewrite this in exponential form:

Now we can find "I" by using our calculators to raise 10 to the -0.9 power. (I'll leave this step up to you.)
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