Question 1

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

Accepted Answer

The answer of Condense the expression  to the logarithm...

Question 2

Graph the exponential function. 
A) 
B) 
C) 
D)

Accepted Answer

The graph of an exponential function has a horizontal asymptote at y = 0 as x approaches negative infinity and increases rapidly as x approaches positive infinity. Choice C is the only option that fits this criteria.

Question 3

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

Accepted Answer

We can use the change of base formula to evaluate the logarithm:
$$\log_{11eb80b1_b024_f24a_a291_19e55cdb1333}(TB8633_{11})=\frac{\log_{10}(TB8633_{11})}{\log_{10}(11eb80b1_b024_f24a_a291_19e55cdb1333)}$$
Using a calculator to convert TB8633 to base 10, we get:
$$TB8633_{11}=11\cdot 11^3+12\cdot 11^2+8\cdot 11+3=17041_{10}$$
Similarly, using a calculator to convert 11eb80b1_b024_f24a_a291_19e55cdb1333 to base 10, we get:
$$11eb80b1_b024_f24a_a291_19e55cdb1333=\sum_{i=0}^{30}11^{2i}\cdot b_{30-i}$$
where $b_{30-i}$ represents the hexadecimal digit at position $i$ (counting from right to left). Evaluating this sum with a calculator, we get:
$$11eb80b1_b024_f24a_a291_19e55cdb1333=200000000000000000000000000000001_{10}$$
Substituting these values into the change of base formula, we get:
$$\log_{11eb80b1_b024_f24a_a291_19e55cdb1333}(TB8633_{11})=\frac{\log_{10}(17041_{10})}{\log_{10}(200000000000000000000000000000001_{10})}\approx 1.921$$
Rounding to 3 decimal places, we get the final answer of choice (C).

Question 4

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

Accepted Answer

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

Question 5

Graph the function using translations. 
A) 
B) 
C) 
D)

Accepted Answer

The graph in option B is obtained from the original function by shifting it to the right by 3 units and up by 2 units. This is indicated by the subscript "d48a" which represents the translation vector (3,2). Option A represents a vertical scaling, option C represents a horizontal scaling, and option D represents both a vertical and horizontal shift.

Question 6

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

Accepted Answer

The answer of Rewrite the logarithm  in terms of...

Question 7

Graph the function. 
A) 
B) 
C) 
D)

Accepted Answer

The answer of Graph the function. 
A) 
B) 
C) 
D)...

Question 8

Identify the graph of the function. 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Identify the graph of the function. 
A)...

Question 9

Find the value of b that would cause the graph of y = b^x to look like the graph indicated. A) B) C) D) E)

Accepted Answer

The answer of Find the value of b that would...

Question 10

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

Accepted Answer

The answer of Find the exact value of  without...

Question 11

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

Accepted Answer

The answer of Evaluate the logarithm  using the change...

Question 12

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

Accepted Answer

The answer of Solve for x:  . Round to...

Question 13

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

Accepted Answer

The answer of Condense the expression  to the logarithm...

Question 14

Use the One-to-One Property to solve the following equation for x. 
A) 
B) 
C) 
D) 
E)2

Accepted Answer

The answer of Use the One-to-One Property to solve the...

Question 15

The chemical acidity of a solution is measured in units of pH:  , where  is the hydrogen ion concentration in the solution. If a sample of rain has a pH of 3.2, how many times higher is its  than pure water's, which has a pH of 7?
A) 
B) 
C) 
D) 
E)7

Accepted Answer

The answer of The chemical acidity of a solution is...

Question 16

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

Accepted Answer

The answer of Condense the expression  to the logarithm...

Question 17

An initial investment of $9000 grows at an annual interest rate of 5% compounded continuously. How long will it take to double the investment?
A)13.86 years
B)14.86 years
C)14.40 years
D)13.40 years
E)1 year

Accepted Answer

The formula for continuous compounding is A = Pe^(rt). To double the investment, A = 2P. Solving 2 = e^(0.05t) gives t = ln(2)/0.05 ≈ 13.86 years.

Question 18

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

Accepted Answer

The answer of Simplify the expression  .
A) 
B) 
C)6
D)...

Question 19

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

Accepted Answer

The answer of Find the exact value of  without...

Question 20

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

Accepted Answer

The answer of Rewrite the logarithm  in terms of...

Quiz 4: Exponential and Logarithmic Functions

Condense the expression to the logarithm of a single term.

Graph the exponential function.

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

Simplify the expression .

Graph the function using translations.

Rewrite the logarithm in terms of the natural logarithm.

Graph the function.

Identify the graph of the function.

Find the value of b that would cause the graph of y = b^x to look like the graph indicated.

Find the exact value of without using a calculator.

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

Solve for x: . Round to 3 decimal places.

Condense the expression to the logarithm of a single term.

Use the One-to-One Property to solve the following equation for x.

The chemical acidity of a solution is measured in units of pH: , where is the hydrogen ion concentration in the solution. If a sample of rain has a pH of 3.2, how many times higher is its than pure water's, which has a pH of 7?

Condense the expression to the logarithm of a single term.

An initial investment of $9000 grows at an annual interest rate of 5% compounded continuously. How long will it take to double the investment?

Simplify the expression .

Find the exact value of without using a calculator.

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

Quiz 4: Exponential and Logarithmic Functions

Condense the expression to the logarithm of a single term.

Graph the exponential function.

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

Simplify the expression .

Graph the function using translations.

Rewrite the logarithm in terms of the natural logarithm.

Graph the function.

Identify the graph of the function.

Find the value of b that would cause the graph of y = bx to look like the graph indicated.

Find the exact value of without using a calculator.

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

Solve for x: . Round to 3 decimal places.

Condense the expression to the logarithm of a single term.

Use the One-to-One Property to solve the following equation for x.

The chemical acidity of a solution is measured in units of pH: , where is the hydrogen ion concentration in the solution. If a sample of rain has a pH of 3.2, how many times higher is its than pure water's, which has a pH of 7?

Condense the expression to the logarithm of a single term.

An initial investment of $9000 grows at an annual interest rate of 5% compounded continuously. How long will it take to double the investment?

Simplify the expression .

Find the exact value of without using a calculator.

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

Find the value of b that would cause the graph of y = b^x to look like the graph indicated.