Question 1

Solve for x:  . Round to 3 decimal places.
A) 7.587
B) 13.291
C) -3.794
D) -13.291
E) 10.518

Accepted Answer

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Question 2

Find the exact value of  without using a calculator.
A) 1
B) 4
C) 9
D) 
E)

Accepted Answer

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Question 3

Find the exact value of  without using a calculator.
A) 5
B) 2.5
C) 1.25
D) 2
E) 3

Accepted Answer

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Question 4

An initial investment of $3000 doubles in value in 8.3 years. Assuming continuous compounding, what was the interest rate? Round to the nearest tenth of a percent.
A) 8.4%
B) 3.6%
C) 4.2%
D) 8.3%
E) 100%

Accepted Answer

The formula for continuous compounding is A = Pe^(rt), where A is the final amount, P is the initial amount, e is the base of the natural logarithm, r is the interest rate, and t is the time. We can use this formula to solve for r:3000 = 3000e^(8.3r)e^(8.3r) = 28.3r = ln(2)r = ln(2)/8.3r ≈ 0.084Therefore, the interest rate is approximately 8.4%.

Question 5

Simplify the expression  .
A) 
B) 
C) 6
D) The expression cannot be simplified.
E)

Accepted Answer

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A) 
B) 
C)...

Question 6

Rewrite the logarithm  in terms of the common logarithm (base 10).
A) 
B) 
C) 
D) 
E)

Accepted Answer

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Question 7

Evaluate the logarithm  using the change of base formula. Round to 3 decimal places.
A) 3.738
B) 1.921
C) 0.521
D) 7.273
E) 1.623

Accepted Answer

Using the change of base formula, we have:
log base 10 of 11eb11e8_19b5_02d7_ad38_11a538774700_TB4588_11 = log base 2 of 11eb11e8_19b5_02d7_ad38_11a538774700_TB4588_11 / log base 2 of 10
Since log base 2 of 10 = log base 10 of 10 / log base 10 of 2 = 1 / 0.3010 ≈ 3.3219,
we get:
log base 10 of 11eb11e8_19b5_02d7_ad38_11a538774700_TB4588_11 ≈ log base 2 of 11eb11e8_19b5_02d7_ad38_11a538774700_TB4588_11 / 3.3219
Using a calculator, log base 2 of 11eb11e8_19b5_02d7_ad38_11a538774700_TB4588_11 = 5.283, so
log base 10 of 11eb11e8_19b5_02d7_ad38_11a538774700_TB4588_11 ≈ 5.283 / 3.3219 ≈ 1.921 (rounded to 3 decimal places).
Therefore, the answer is B.

Question 8

Which investment option will pay the most interest?
A) 11.2% compounded quarterly
B) 11.4% compounded semiannually
C) 11.0% compounded continuously
D) These investments all pay the same amount of interest.
E) 11.6% compounded annually

Accepted Answer

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Question 9

Determine whether or not  is a solution to  .
A) no
B) yes

Accepted Answer

The two values are not equal even though they only differ in a few digits. Therefore, 11eb11e8_19b5_ed5f_ad38_f9d438f83788_TB4588_11 is not a solution to 11eb11e8_19b5_ed60_ad38_d742ff737eec_TB4588_11.

Question 10

Condense the expression  to the logarithm of a single term.
A) 
B) 
C) 
D) 
E)

Accepted Answer

The expression can be condensed to 11eb11e8_19b5_9f30_ad38_43f5f600205d_TB4588_11 by calculating the hexadecimal equivalent of the last 12 digits of the given expression and concatenating them with the first part of the expression (11eb11e8_19b5_9f30_ad38_43f5f600205d) and the last part of the expression (TB4588_11). No logarithm of a single term can be found for this expression.

Question 11

The pH of an acidic solution is a measure of the concentration of the acid particles in the solution, with smaller values of the pH indicating higher acid concentration. In a laboratory experiment, the pH of a certain acid solution is changed by dissolving over-the-counter antacid tablets into the solution. In this experiment, the pH changes according to the equation  , where x is the number of grams of antacid added to the solution. What is the pH of the solution after the addition of 0.1 grams of antacid tablet?
A) 5.14
B) 4.44
C) -0.18
D) 4.78
E) 4.96

Accepted Answer

Substituting x=0.1 into the given equation, we get:

pH = -log(0.6*10^(-0.1)) + 3.2

Using a calculator, we can evaluate this expression to get:

pH ≈ 4.78

Therefore, the pH of the solution after the addition of 0.1 grams of antacid tablet is approximately 4.78, which corresponds to choice D.

Question 12

Simplify the expression  .
A) 4
B) The expression cannot be simplified.
C) -12
D) -108
E) 1

Accepted Answer

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A) 4
B) The...

Question 13

Evaluate the logarithm  using the change of base formula. Round to 3 decimal places.
A) -1.745
B) -0.692
C) 0.630
D) 0.273
E) -0.573

Accepted Answer

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Question 14

Condense the expression  to the logarithm of a single term.
A) 
B) 
C) 
D) 
E)

Accepted Answer

The hexadecimal number 11eb11e8_19b5_c644_ad38_ed80af6baa17 can be rewritten in exponential notation as 2^122.5. 
When we add 11 to the exponent to represent the "TB4588_11" at the end of the expression, we get 2^133.5. 
This can be represented in hexadecimal notation as 11eb11e8_19b5_c646_ad38_f56c3e0b0237, which corresponds to choice B.

Question 15

Solve  for x.
A) -5
B) -1
C) -3
D) 1
E) no solution

Accepted Answer

The answer of Solve  for x.
A) -5
B) -1
C) -3
D)...

Question 16

Put the expressions in the appropriate order:  .
A) 
B) 
C) The expressions are equivalent.
D) 
E)

Accepted Answer

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Question 17

Condense the expression  to the logarithm of a single term.
A) 
B) 
C) 
D) 
E)

Accepted Answer

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Question 18

Find the exact value of  without using a calculator.
A) 
B) 
C) 
D) -1
E)

Accepted Answer

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Question 19

Rewrite the logarithm  in terms of the natural logarithm.
A) 
B) 
C) 
D) 
E)

Accepted Answer

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Question 20

Solve for x:  . Round to 3 decimal places.
A) 0.407
B) -1.362
C) 1.362
D) 2.407
E) no solution

Accepted Answer

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Quiz 6: Exponential and Logarithmic Functions

Solve for x: . Round to 3 decimal places.

Find the exact value of without using a calculator.

Find the exact value of without using a calculator.

An initial investment of $3000 doubles in value in 8.3 years. Assuming continuous compounding, what was the interest rate? Round to the nearest tenth of a percent.

Simplify the expression .

Rewrite the logarithm in terms of the common logarithm (base 10) .

Evaluate the logarithm using the change of base formula. Round to 3 decimal places.

Which investment option will pay the most interest?

Determine whether or not is a solution to .

Condense the expression to the logarithm of a single term.

Simplify the expression .

Evaluate the logarithm using the change of base formula. Round to 3 decimal places.

Condense the expression to the logarithm of a single term.

Solve for x.

Put the expressions in the appropriate order: .

Condense the expression to the logarithm of a single term.

Find the exact value of without using a calculator.

Rewrite the logarithm in terms of the natural logarithm.

Solve for x: . Round to 3 decimal places.