To learn the properties of logarithms and how to manipulate them when solving so

Question

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/m^2 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/m^2 and wo begin to feel pain when the intensity reaches 1 W/m^2. 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 beta, which is measured in decibels (dB), For a given sound intensity I, beta is found from the equation beta =(10 dB)log(I/I_0). where I_0 = 1.0 times 10^12 W/m^2 The power in the speaker from Part A is doubled bringing the sound intensity to 2 times 10^-6 W/m^2 T his leads to beta = 10 log (2 times 10^6) Which of the following equations is equivalent to Iog(2 times 10^6)? log(2) times Iog(10^6) log(2) + Iog(10^6) 2 times Iog(10^6) 2 + log(10^6) log(10^6) + log(10^6) 6 times Iog(20) This question will be shown after you complete previous question(s).

Explanation / Answer

Here ,

for log(m^n) = n * log(m)

and log(m * n) = log(m) + log(n)

Now , for log(2 *10^6)

= log(2) + log(10^6)

the correct option is 2

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