The answer would be A because the theorem is not proven as true and reliable <span />
Problem 1)
The base of the exponential is 12 which is also the base of the log as well. The only answer choice that has this is choice B.
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Problem 2)
log(x) + log(y) - 2log(z)
log(x) + log(y) - log(z^2)
log(x*y) - log(z^2)
log[(x*y)/(z^2)]
Answer is choice D
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Problem 3)
log[21/(x^2)]
log(21) - log(x^2)
log(21) - 2*log(x)
This matches with choice B
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Problem 4)
Ln(63) = Ln(z) + Ln(7)
Ln(63)-Ln(7) = Ln(z)
Ln(63/7) = Ln(z)
Ln(9) = Ln(z)
z = 9
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Problem 5)
Ln(5x-3) = 2
5x-3 = e^2
5x = e^2+3
x = (e^2+3)/5
This means choice A is the answer
This is the standard form equation 
What is the ellipse?
The equation for an ellipse is typically written as x² a² + y² b² = 1. x² a² + y² b² = 1. An ellipse with its origin at the center is defined by this equation. The ellipse is stretched further in both the horizontal and vertical directions if a > b, a > b, and if b > a, b > a, respectively.
The standard form of the equation of an ellipse with center (h, k)and major axis parallel to the x-axis is:

where,
a > b
the length of the major axis is 2a
the coordinates of the vertices are (h±a,k)
the length of the minor axis is 2b
the coordinates of the co-vertices are (h,k±b)
the coordinates of the foci are (h±c,k),
where c² = a² − b².
so,

Hence, this is the standard form equation
.
To learn more about ellipse, visit
brainly.com/question/16904744
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Answer:
The above mentioned qualities go under the category of abilities.
Step-by-step explanation:
Lily does a self-inventory to find out theat she has knowledge of Excel , proficiency in bookkeeping and training in customer service .
Ability is used to refer a person's native aptitude in a specific field.
Ability can also be trained and honed and can be made better with practice.
All of Lily's qualities mentioned come under the same above mentioned specifications. All her talents can be trained and can be bettered.
Hence her qualities come under the category of abilities.
A.) The circumference of the tire is 94.2
B.) The tire will have to rotate 56 times to
travel 1 mile.