Question

3. A company with loud machinery needs to cut its sound intensity to 44% of its original level. By how many decibels would the loudness be reduced? Use the formula L=10log I/I(o). Round to the nearest hundredth.
A) 3.57 decibels *answer*
B) 1.58 decibels
C) 2.52 decibels
D) 1.93 decibels


6. Write the expression as a single natural logarithm.
2 In x-5 In c

A. In(x2+c5)
B. In x2/c5 *answer*
C. In(x2-c5)
D. inx2c5

Answer 1

Answer:   3.   The correct option is:  A) 3.57 decibels.

6.   The correct option is:  B) $ln(\frac{x^2}{c^5})$

Step-by-step explanation:

3.    Sound intensity is cut to 44% of its original level. That means, if the original sound intensity was 100, then now sound intensity will be 44.

So,  $I_{0}= 100$ and $I= 44$

Using the formula $L= 10log(\frac{I}{I_{0}})$, we will get.....

$L= 10log(\frac{44}{100})\\ \\ L= 10log(0.44)\\ \\ L= 10(-0.3565...)=-3.565...\approx -3.57$

(Rounded to the nearest hundredth)

So, the loudness would be reduced by 3.57 decibels.

6.    Given expression is:    $2ln(x) - 5ln(c)$

First applying the property $m*log(x)= log(x^m)$ , we will get.....

$ln(x^2)-ln(c^5)$

Now using the formula, $log(a)-log(b)= log(\frac{a}{b})$, we will get....

$ln(x^2)-ln(c^5) = ln(\frac{x^2}{c^5})$

Thus, the answer as a single natural logarithm is   $ln(\frac{x^2}{c^5})$