Answer: 3. The correct option is: A) 3.57 decibels.
6. The correct option is: B) [tex]ln(\frac{x^2}{c^5})[/tex]
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, [tex]I_{0}= 100[/tex] and [tex]I= 44[/tex]
Using the formula [tex]L= 10log(\frac{I}{I_{0}})[/tex], we will get.....
[tex]L= 10log(\frac{44}{100})\\ \\ L= 10log(0.44)\\ \\ L= 10(-0.3565...)=-3.565...\approx -3.57[/tex]
(Rounded to the nearest hundredth)
So, the loudness would be reduced by 3.57 decibels.
6. Given expression is: [tex]2ln(x) - 5ln(c)[/tex]
First applying the property [tex]m*log(x)= log(x^m)[/tex] , we will get.....
[tex]ln(x^2)-ln(c^5)[/tex]
Now using the formula, [tex]log(a)-log(b)= log(\frac{a}{b})[/tex], we will get....
[tex]ln(x^2)-ln(c^5) = ln(\frac{x^2}{c^5})[/tex]
Thus, the answer as a single natural logarithm is [tex]ln(\frac{x^2}{c^5})[/tex]
The expression of both questions from natural logarithm are; A) 3.57 Decibels and B) In (x²/c⁵)
5) We are told that;
Sound intensity is cut to 44% of its original level.
Thus, ratio of new sound intensity to original sound intensity is 44/100.
We are given the formula;
L = 10 log (I/I₀)
Thus;
L = 10 Log (44/100)
L = 3.57
6) We are given the expression;
2 Inx - 5 In c
From property of exponents, we can express as;
In (x²) - In (c⁵)
ALso from division property of exponents, theis gives us;
In (x²/c⁵)
Read more about Natural logarithm at; https://brainly.com/question/2732137
