Multiple Choice Expand the logarithmic expression. log8 (1 point) Responses log82 – log8a log 8 2 – log 8 a Image with alt text: start fraction log subscript 8 baseline a over log subscript 8 baseline 2 end fraction log8a – log82 log 8 a – log 8 2 –a log82
The correct answer is: log8a - log82
Use the Change of Base Formula to evaluate log877. (1 point) Responses 3.467 3.467 1.886 1.886 4.344 4.344 2.089
The correct answer is: 3.467
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 . Round to the nearest hundredth. (1 point) Responses 3.57 decibels 3.57 decibels 1.58 decibels 1.58 decibels 2.52 decibels 2.52 decibels 1.93 decibels 1.93 decibels
To calculate the reduction in decibels, you can use the formula:
Decibel reduction = 10 * log10(Intensity ratio)
In this case, the intensity ratio is 44% or 0.44 (since it needs to be reduced to 44% of its original level).
Using this information, we can calculate as follows:
Decibel reduction = 10 * log10(0.44)
≈ 10 * -0.3562
≈ -3.562
So, rounding to the nearest hundredth, the reduction in decibels would be approximately 3.57 decibels.
Therefore, the correct answer is: 3.57 decibels.
Use a table to solve. Round to the nearest hundredth. 28x = 93 (1 point) Responses 0.82 0.82 30.72 30.72 3.14 3.14 52.31
To solve the equation 28x = 93 using a table, we can create a table and substitute different values for x until we find a value that satisfies the equation:
x | 28x
--------------
1 | 28
2 | 56
3 | 84
4 | 112
5 | 140
Looking at the table, we can see that for x = 4, we get a value close to 93. Let's do a more precise calculation:
28 * 4 = 112
Since 112 is greater than 93, we know that x must be slightly smaller than 4. We can estimate it by using the next value in the table:
28 * 3 = 84
Now, let's find a value between 3 and 4 that gives us a result close to 93:
28 * 3.1 = 86.8
28 * 3.2 = 89.6
28 * 3.14 = 87.92
From the calculations, we can see that 28 * 3.14 is the closest value to 93.
Therefore, rounding to the nearest hundredth, the solution to the equation 28x = 93 is approximately x = 3.14.
So, the correct answer is: 3.14.
Solve log 2x + log 12 = 3. Round to the nearest hundredth if necessary. (1 point) Responses 6,000 6,000 24,000 24,000 166.67 166.67 41.67
To solve the equation log(2x) + log(12) = 3, we can use logarithmic properties.
Using the product rule of logarithms, we can simplify the equation as follows:
log(2x * 12) = 3
Simplifying further:
log(24x) = 3
Now, we can rewrite the equation in exponential form:
10^3 = 24x
Solving for x, we have:
1000 = 24x
Dividing both sides by 24:
x ≈ 41.67
Rounding to the nearest hundredth, the solution to the equation log(2x) + log(12) = 3 is approximately x = 41.67.
So, the correct answer is: 41.67.