Question 998792: Please Help and Show All Steps
the loudness of sound is measured in decibels. These units are measured by first assigning an intensity I_0 to a very soft sound (which is called the threshold sound). The sound we wish to measure is assigned an intensity I, and we measure the decibel rating d of this sound with the equation: d=10log^I/I_0.
Find the loudness, in decibels, or each sound with given intensity:
A) Study Lounge (I=2500*I_0) the answer I got was 40864.32
B) Normal Concentration (I=10^6*I_0)= my answer 100004
C) Dishwasher (I=2500000*I_0)= my answer 393.0
D) Rock Concert (I=10^12*I_0)=my answer 25,000,000,000.43
E) Exposure to sounds above 85 decibels may cause permanent hearing loss... should we avoid any of the above? I put rock concert and dishwasher
Answer by josgarithmetic(39618)   (Show Source):
You can put this solution on YOUR website! You really mean,  .
After that, your items to answer are incomplete. You show a given I value, but your needed  value is missing or something. Maybe, you mean it they way they look. Not sure.
(A)
The log input seems to be  . It just looks strange. This would mean, 
 .
The rest of your items are all of the same form and so you will treat them the same way. (Item E is different but only relies on good judgement about avoiding damaging noise).
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Recheck your given formula for d.
Factor of 10, factor of Natural Logarithm of (I divided by I sub zero).
The question part (A) gives you I equals 2500 multiplied by I sub zero. This will mean (you recheck the arithmetic or the algebra) that your expression to evaluate is : Factor of 10, factor of Natural Logarithm of 2500.
Use scientific calculator, or graphing calculator, or table of logarithms.
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NOW, be reminded, the exprssion you want to compute is 
Best is to keep with just two significant figures here because that is the best accuracy that you have in the given data, so,
 .
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For B, C, and D, JUST FOLLOW THE FORMULA.
C,
 --------------or 147, if to three significant figures
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