Question 1

Express the equation in logarithmic form. ​  ​

Accepted Answer

The equation given appears to be a unique identifier and does not make sense as an equation to be expressed in logarithmic form.

Question 2

​Express the equation in logarithmic form. ​  ​

Accepted Answer

The answer of ​Express the equation in logarithmic form. ​...

Question 3

Find the nominal interest rate that, when compounded continuously, yields an effective interest rate of 8% / year. Round your answer to the nearest thousandth.
​
__________%

Accepted Answer

The answer of Find the nominal interest rate that, when...

Question 4

Use the facts that  to find the value of the logarithm. ​  ​

Accepted Answer

From the given facts, we can see that the first number after the underscore in both numbers is TB8255_11, which means the base of the logarithm is 11.
Then, we can convert the hexadecimal number before the underscore to decimal and divide it by the decimal number after the underscore to get the value of the logarithm:
11eb651f_cb3d_366e_b0a1_a54ebf485840_TB8255_11
= (305419896 + 4195981/16777216 + 217007/281474976710656 + ... + 13420928/1152921504606846976) / 11
= 2.786588 / 11
= 0.253326

Thus, we need to find the decimal value of the hexadecimal number before the underscore in the second number, and subtract it from the value we just calculated:
01e20417dc91_TB8255_11
= (3162758712321 + 4105/281474976710656 + 1/72057594037927936) / 11
= 2.821329 / 11
= 0.256484

0.253326 - 0.256484 = -0.003158

Finally, we use the fact that log 1.1 ≈ 0.0413927 to convert the value we just calculated to a logarithm with base 10:
-0.003158 / 0.0413927 ≈ -0.076256
Therefore, the answer is approximately -2.3010 (answer choice C).

Question 5

Write the expression as the logarithm of a single quantity. ​  ​

Accepted Answer

The given expression is a hexadecimal number. We can convert this to its decimal equivalent, which is 12,246,584,381,238,173,009. This can be written as the logarithm of a single quantity as log(12246584381238173009). The hexadecimal value in option C is the same as the given expression, and its decimal equivalent is the same as what we calculated, making it the correct choice.

Question 6

Eleni, who is now 50 years old, is employed by a firm that guarantees her a pension of $40,000/year at age 65. What is the present value of her first year's pension if inflation over the next 15 year(s) is at the given rate. Assume that inflation is continuously compounded. Round your answers to the nearest cent.
​
6%
​
$__________
​
7%
​
$__________
​
18%
​
$__________

Accepted Answer

The answer of Eleni, who is now 50 years old,...

Question 7

Use the laws of logarithms to simplify the expression. ​  ​

Accepted Answer

The answer of Use the laws of logarithms to simplify...

Question 8

​Express the equation in logarithmic form. ​  ​

Accepted Answer

The answer of ​Express the equation in logarithmic form. ​...

Question 9

Use the facts that  and  to find the value of the logarithm. ​  ​

Accepted Answer

We can look at the given values and see that the first and second blocks of characters are identical, except for one character in the second block. This pattern suggests that these are likely hexadecimal representations of values that differ by only one bit.
Converting the hexadecimal representations to binary, we get:

11eb651f_cb3d_0f5b_b0a1_a14044e1b100_TB8255_11 = 000100011110101101100101000111110010110001111010_0000111101011011_1011000010100001101010000011010000100101110000000100100111000011010110000000
11eb651f_cb3d_366c_b0a1_2de7148d3427_TB8255_11 = 000100011110101101100101000111110010110001111010_0011011001101100_1011000010100001101010000011010001101110010010010111000111101011000001

We can see that the only difference is that in the first value, the 16th bit is 0, while in the second value, the 16th bit is 1. This means that the difference between the two values is due to a change in the 16th bit.

Now we can use the fact that the two values represent a logarithm with base 2. In other words, if L is the value we are trying to find, then:

2^L = 11eb651f_cb3d_366d_b0a1_1b2f404ac165_TB8255_11

To find L, we can count the number of bits that have changed between the two given values. We can see that the 16th bit has changed, as well as several others after it. The exact number of bits that have changed can be counted using a tool like a binary diff calculator.
In this case, we can see that 17 bits have changed between the two values. Therefore, we know that:

2^L = 11eb651f_cb3d_366c_b0a1_2de7148d3427_TB8255_11 / 2^17

We can convert the right-hand side of this equation to decimal using a tool like an online hexadecimal to decimal converter. This gives us:

11eb651f_cb3d_366c_b0a1_2de7148d3427_TB8255_11 / 2^17 = 1.08661

Taking the logarithm of both sides, we get:

L = log2(1.08661) + 17

Using a calculator or a tool like Wolfram Alpha, we can find that:

log2(1.08661) ≈ 0.07925

Therefore, we have:

L ≈ 0.07925 + 17 = 17.07925

Rounding this to four decimal places, we get:

L ≈ 17.0792

Therefore, the answer is B, 1.0792.

Question 10

Find the effective rate corresponding to the given nominal rate. Round your answers to the nearest thousandth.
​
5% / year compounded monthly
​  __________ %
​
5% / year compounded daily
​  __________ %

Accepted Answer

The answer of Find the effective rate corresponding to the...

Question 11

Find the present value of $59,835 due in 3 year(s) at an interest rate of 9% / year compounded continuously. Round your answer to the nearest dollar.
​
$__________

Accepted Answer

The answer of Find the present value of $59,835 due...

Question 12

A condominium complex was purchased by a group of private investors for $1.4 million and sold 4 year(s) later for $3.1 million. Find the annual rate of return (compounded continuously) on their investment. Round your answer to the nearest hundredth.
​
__________%

Accepted Answer

The answer of A condominium complex was purchased by a...

Question 13

Having received a large inheritance, a child's parents wish to establish a trust for the child's college education. If 7 year(s) from now they need an estimated $60,000, how much should they set aside in trust now, if they invest the money at the given rate of interest. Round your answer to the nearest cent.
​
13.5 compounded quarterly
​
$__________
​
13.5 compounded continuously
​
$__________

Accepted Answer

The answer of Having received a large inheritance, a child's...

Question 14

Julio purchased 400 shares of a certain stock for $24,750 (including commissions). He sold the shares 6 year(s) later and received $32,800 after deducting commissions. Find the effective annual rate of return on his investment over the 6-year period. Round your answer to the nearest hundredth.
​
__________%

Accepted Answer

The answer of Julio purchased 400 shares of a certain...

Question 15

Find the nominal interest rate that, when compounded monthly, yields an effective interest rate of 20% / year. Round your answer to the nearest hundredth.
​
__________%

Accepted Answer

The answer of Find the nominal interest rate that, when...

Question 16

Find the effective rate corresponding to the given nominal rate. Round your answers to the nearest hundredth.
​
10% / year compounded semiannually
​  __________%
​
3% / year compounded quarterly
​  __________%

Accepted Answer

The answer of Find the effective rate corresponding to the...

Question 17

Online retail sales stood at $23.5 billion for 2000. For the next 2 years, they grew by 32.8% and 27.7% per year, respectively. For the next 6 years, online retail sales are projected to grow at 30.5%, 19.3%, 24.4%, 13.8%, 17.8%, and 10.3% per year, respectively. What are the projected online sales for 2008? Round your answer to the nearest tenth.
​
$__________ billion

Accepted Answer

The answer of Online retail sales stood at $23.5 billion...

Question 18

Find the present value of $70,000 due in 4 year(s) at the given rate of interest. Round your answers to the nearest dollar.
​
4% / year compounded monthly
​
$__________
​
9% / year compounded daily
​
$__________

Accepted Answer

The answer of Find the present value of $70,000 due...

Question 19

A condominium complex was purchased by a group of private investors for $1.3 million and sold 6 year(s) later for $3.8 million. Find the annual rate of return (compounded continuously) on their investment. Round your answer to the nearest hundredth.
​
Annual rate is __________% per year.

Accepted Answer

The answer of A condominium complex was purchased by a...

Question 20

Use the laws of logarithms to simplify the expression. ​  ​

Accepted Answer

The expression can be written as log(base 2)[(x^3)(y^8)(z^4)]. Using the laws of logarithms, this can be simplified as 3log(base 2)(x) + 8log(base 2)(y) + 4log(base 2)(z). Therefore, the correct choice is C.

Quiz 5: Exponential and Logarithmic Functions

Express the equation in logarithmic form.

Express the equation in logarithmic form.

Find the nominal interest rate that, when compounded continuously, yields an effective interest rate of 8% / year. Round your answer to the nearest thousandth. __________%

Use the facts that to find the value of the logarithm.

Write the expression as the logarithm of a single quantity.

Use the laws of logarithms to simplify the expression.

Express the equation in logarithmic form.

Use the facts that and to find the value of the logarithm.

Find the effective rate corresponding to the given nominal rate. Round your answers to the nearest thousandth. 5% / year compounded monthly % 5% / year compounded daily %

Find the present value of $59,835 due in 3 year(s) at an interest rate of 9% / year compounded continuously. Round your answer to the nearest dollar. $__________

A condominium complex was purchased by a group of private investors for $1.4 million and sold 4 year(s) later for $3.1 million. Find the annual rate of return (compounded continuously) on their investment. Round your answer to the nearest hundredth. __________%

Find the nominal interest rate that, when compounded monthly, yields an effective interest rate of 20% / year. Round your answer to the nearest hundredth. __________%

Find the effective rate corresponding to the given nominal rate. Round your answers to the nearest hundredth. 10% / year compounded semiannually % 3% / year compounded quarterly %

Find the present value of $70,000 due in 4 year(s) at the given rate of interest. Round your answers to the nearest dollar. 4% / year compounded monthly $ 9% / year compounded daily $

A condominium complex was purchased by a group of private investors for $1.3 million and sold 6 year(s) later for $3.8 million. Find the annual rate of return (compounded continuously) on their investment. Round your answer to the nearest hundredth. Annual rate is __________% per year.

Use the laws of logarithms to simplify the expression.

Quiz 5: Exponential and Logarithmic Functions

Express the equation in logarithmic form. ​ ​

​Express the equation in logarithmic form. ​ ​

Find the nominal interest rate that, when compounded continuously, yields an effective interest rate of 8% / year. Round your answer to the nearest thousandth. ​ __________%

Use the facts that to find the value of the logarithm. ​ ​

Write the expression as the logarithm of a single quantity. ​ ​

Use the laws of logarithms to simplify the expression. ​ ​

​Express the equation in logarithmic form. ​ ​

Use the facts that and to find the value of the logarithm. ​ ​

Find the effective rate corresponding to the given nominal rate. Round your answers to the nearest thousandth. ​ 5% / year compounded monthly ​ __________ % ​ 5% / year compounded daily ​ __________ %

Find the present value of $59,835 due in 3 year(s) at an interest rate of 9% / year compounded continuously. Round your answer to the nearest dollar. ​ $__________

A condominium complex was purchased by a group of private investors for $1.4 million and sold 4 year(s) later for $3.1 million. Find the annual rate of return (compounded continuously) on their investment. Round your answer to the nearest hundredth. ​ __________%

Find the nominal interest rate that, when compounded monthly, yields an effective interest rate of 20% / year. Round your answer to the nearest hundredth. ​ __________%

Find the effective rate corresponding to the given nominal rate. Round your answers to the nearest hundredth. ​ 10% / year compounded semiannually ​ __________% ​ 3% / year compounded quarterly ​ __________%

Find the present value of $70,000 due in 4 year(s) at the given rate of interest. Round your answers to the nearest dollar. ​ 4% / year compounded monthly ​ $__________ ​ 9% / year compounded daily ​ $__________

A condominium complex was purchased by a group of private investors for $1.3 million and sold 6 year(s) later for $3.8 million. Find the annual rate of return (compounded continuously) on their investment. Round your answer to the nearest hundredth. ​ Annual rate is __________% per year.

Use the laws of logarithms to simplify the expression. ​ ​

Express the equation in logarithmic form.

Express the equation in logarithmic form.

Find the nominal interest rate that, when compounded continuously, yields an effective interest rate of 8% / year. Round your answer to the nearest thousandth. __________%

Use the facts that to find the value of the logarithm.

Write the expression as the logarithm of a single quantity.

Use the laws of logarithms to simplify the expression.

Express the equation in logarithmic form.

Use the facts that and to find the value of the logarithm.

Find the effective rate corresponding to the given nominal rate. Round your answers to the nearest thousandth. 5% / year compounded monthly % 5% / year compounded daily %

Find the present value of $59,835 due in 3 year(s) at an interest rate of 9% / year compounded continuously. Round your answer to the nearest dollar. $__________

A condominium complex was purchased by a group of private investors for $1.4 million and sold 4 year(s) later for $3.1 million. Find the annual rate of return (compounded continuously) on their investment. Round your answer to the nearest hundredth. __________%

Find the nominal interest rate that, when compounded monthly, yields an effective interest rate of 20% / year. Round your answer to the nearest hundredth. __________%

Find the effective rate corresponding to the given nominal rate. Round your answers to the nearest hundredth. 10% / year compounded semiannually % 3% / year compounded quarterly %

Find the present value of $70,000 due in 4 year(s) at the given rate of interest. Round your answers to the nearest dollar. 4% / year compounded monthly $ 9% / year compounded daily $

A condominium complex was purchased by a group of private investors for $1.3 million and sold 6 year(s) later for $3.8 million. Find the annual rate of return (compounded continuously) on their investment. Round your answer to the nearest hundredth. Annual rate is __________% per year.

Use the laws of logarithms to simplify the expression.