Question 1

Use properties of logarithms to evaluate the expression.
-$1000 ^ { \log _ { 10 } 8 }$

Accepted Answer

A)  $10 ^ { 24 }$ 
B)  512 
C)  24 
D)  $\log 512$ 
A)  $10 ^ { 24 }$ 
B)  512 
C)  24 
D)  $\log 512$

Question 2

The population of a particular city is increasing at a rate proportional to its size. It follows the function P(t) = 1 + ke0.08t where k is a constant and t is the time in years. If the current population is 22,000, in how many
Years is the population expected to be 55,000? Round to the nearest year.

Accepted Answer

A)  5 yr 
B)  11 yr 
C)  76 yr 
D)  6 yr 
A)  5 yr 
B)  11 yr 
C)  76 yr 
D)  6 yr

Question 3

Find the value. Give an approximation to four decimal places.
-$$\log \left( \frac { 637 } { 368 } \right)$$

Accepted Answer

A)  0.2383 
B)  12.3649 
C)  1.0929 
D)  0.5487 
A)  0.2383 
B)  12.3649 
C)  1.0929 
D)  0.5487

Question 4

Round to the nearest thousandth.
-$$4 ^ { ( x + 3 ) } = 2 ^ { x }$$

Accepted Answer

A)  $\{ - 6.000 \}$ 
B)  $\{ 6.000 \}$ 
C)  $\{ - 7.860 \}$ 
D)  $\{ - 4.140 \}$ 
A)  $\{ - 6.000 \}$ 
B)  $\{ 6.000 \}$ 
C)  $\{ - 7.860 \}$ 
D)  $\{ - 4.140 \}$

Question 5

Suppose that the salinity $S$ of ocean water at a given depth $d$ is modeled by the equation $\mathrm { S } ( \mathrm { d } ) = 31.7 + 1.5 \log ( \mathrm { d } + 1 )$, where $\mathrm { S }$ is measured in grams salt per kilogram water and $\mathrm { d }$ is measured in meters. What is the salinity when the depth is $931 \mathrm {~m}$ ? Round your answer to the nearest hundredth.

Accepted Answer

A)  $- 27.25 \mathrm {~g} \mathrm { salt } / \mathrm { kg }$ water 
B)  $92.63 \mathrm {~g} \mathrm { salt } / \mathrm { kg }$ water 
C)  $95.63 \mathrm {~g} \mathrm { salt } / \mathrm { kg }$ water 
D)  $36.15 \mathrm {~g} \mathrm { salt } / \mathrm { kg }$ water 
A)  $- 27.25 \mathrm {~g} \mathrm { salt } / \mathrm { kg }$ water 
B)  $92.63 \mathrm {~g} \mathrm { salt } / \mathrm { kg }$ water 
C)  $95.63 \mathrm {~g} \mathrm { salt } / \mathrm { kg }$ water 
D)  $36.15 \mathrm {~g} \mathrm { salt } / \mathrm { kg }$ water

Question 6

Find the value. Give an approximation to four decimal places.
-$\log 298 + \log 17$

Accepted Answer

A)  3.7047 
B)  8.5303 
C)  3.0444 
D)  16.1411 
A)  3.7047 
B)  8.5303 
C)  3.0444 
D)  16.1411

Question 7

Write an equivalent expression in exponential form.
-$\log _ { x } 25 = 2$

Accepted Answer

A)  {27} 
B)  {50} 
C)  {5} 
D)  {13} 
A)  {27} 
B)  {50} 
C)  {5} 
D)  {13}

Question 8

Which of the following is the same as $\log ( 12 x ) - \log ( 3 x )$ for $x > 0$ ?

Accepted Answer

A)  $4 \log x$ 
B)  $\frac { \log ( 12 x ) } { \log ( 3 x ) }$ 
C)  $\log ( 4 )$ 
D)  $\log ( 9 x )$ 
A)  $4 \log x$ 
B)  $\frac { \log ( 12 x ) } { \log ( 3 x ) }$ 
C)  $\log ( 4 )$ 
D)  $\log ( 9 x )$

Question 9

Provide an appropriate response.
-The graph of an exponential function with base a is given. Sketch the graph of $h ( x ) = a - x$. Give the domain and range of $h$.
$$f ( x ) = a ^ { x }$$

Accepted Answer

The answer of Provide an appropriate response.
-The graph of an...

Question 10

Evaluate the logarithm.
-$\log _ { 23 } 1$

Accepted Answer

A)  0 
B)  10 
C)  23 
D)  1 
A)  0 
B)  10 
C)  23 
D)  1

Question 11

An earthquake was recorded with an intensity which was 125,893 times more powerful than a reference level earthquake, or 125,893 · I0. What is the magnitude of this earthquake on the Richter scale (rounded to the
Nearest tenth)? Intensity on the Richter scale is log10 $\left( \mathrm { I } / \mathrm { I } _ { 0 } \right)$

Accepted Answer

A)  5.1 
B)  4.1 
C)  0.5 
D)  11.7 
A)  5.1 
B)  4.1 
C)  0.5 
D)  11.7

Question 12

Solve the equation.
-$$m ^ { - 4 } = \frac { 1 } { 81 }$$

Accepted Answer

A)  $\left\{ \frac { 1 } { 3 } \right\}$ 
B)  $\{ 3 \}$ 
C)  $\{ - 3,3 \}$ 
D)  $\{ 81 \}$ 
A)  $\left\{ \frac { 1 } { 3 } \right\}$ 
B)  $\{ 3 \}$ 
C)  $\{ - 3,3 \}$ 
D)  $\{ 81 \}$

Question 13

Write in logarithmic form.
-$$\left( \frac { 5 } { 6 } \right) ^ { 5 } = \frac { 3125 } { 7776 }$$

Accepted Answer

A)  $\log _ { 5 } \left( \frac { 5 } { 6 } \right) = \frac { 3125 } { 7776 }$ 
B)  $\log _ { 5 / 6 } 5 = \frac { 3125 } { 7776 }$ 
C)  $\log _ { 5 / 6 } \left( \frac { 3125 } { 7776 } \right) = 5$ 
D)  $\frac { \log _ { 5 } 3125 } { \log _ { 5 } 7776 } = \frac { 5 } { 6 }$ 
A)  $\log _ { 5 } \left( \frac { 5 } { 6 } \right) = \frac { 3125 } { 7776 }$ 
B)  $\log _ { 5 / 6 } 5 = \frac { 3125 } { 7776 }$ 
C)  $\log _ { 5 / 6 } \left( \frac { 3125 } { 7776 } \right) = 5$ 
D)  $\frac { \log _ { 5 } 3125 } { \log _ { 5 } 7776 } = \frac { 5 } { 6 }$

Question 14

In the formula A(t) = A0ekt, A is the amount of radioactive material remaining from an initial amount A0 at a given time t, and k is a negative constant determined by the nature of the material. A certain radioactive isotope
Decays at a rate of 0.3% annually. Determine the half-life of this isotope, to the nearest year.

Accepted Answer

A)  167 yr 
B)  231 yr 
C)  2 yr 
D)  100 yr 
A)  167 yr 
B)  231 yr 
C)  2 yr 
D)  100 yr

Question 15

Assume the cost of a gallon of milk is $3.40. With continuous compounding, find the time it would take the cost to be 4 times as much (to the nearest tenth of a year), at an annual inflation rate of 6%.

Accepted Answer

A)  0.1 yr 
B)  8.5 yr 
C)  0.0 yr 
D)  23.1 yr 
A)  0.1 yr 
B)  8.5 yr 
C)  0.0 yr 
D)  23.1 yr

Question 16

Use the properties of logarithms to rewrite the expression. Simplify the result if possible. Assume all variables represent positive real numbers.
-$\log _ { 8 } \left( \frac { 4 \sqrt { 7 } } { 8 } \right)$
$\log _ { 8 } 4 + \frac { 1 } { 2 } \log _ { 8 } 7$

Accepted Answer

A)  $\left( \log _ { 8 } 4 \right) \left( \frac { 1 } { 2 } \log _ { 8 } 7 \right) - \log _ { 8 } 8$ 
B)  $\frac { \log 88 } { 2 }$ 
C)  $\log _ { 8 } 4 + \frac { 1 } { 2 } \log _ { 8 } 7 - \log _ { 8 } 8$ 
D)  $\log _ { 8 } 4 + \sqrt { \log _ { 8 } 7 } - \log 88$ 
A)  $\left( \log _ { 8 } 4 \right) \left( \frac { 1 } { 2 } \log _ { 8 } 7 \right) - \log _ { 8 } 8$ 
B)  $\frac { \log 88 } { 2 }$ 
C)  $\log _ { 8 } 4 + \frac { 1 } { 2 } \log _ { 8 } 7 - \log _ { 8 } 8$ 
D)  $\log _ { 8 } 4 + \sqrt { \log _ { 8 } 7 } - \log 88$

Question 17

The decay of 243 mg of an isotope is given by $$\mathrm { A } ( \mathrm { t } ) = 243 \mathrm { e } ^ { - 0.014 \mathrm { t } }$$ where t is time in years since the initial amount of 243 mg was present. Find the amount (to the nearest milligram) left after 72 years.

Accepted Answer

A)  240 
B)  89 
C)  45 
D)  87 
A)  240 
B)  89 
C)  45 
D)  87

Question 18

Find the value. Give an approximation to four decimal places.
-$\ln \sqrt [ 4 ] { \mathrm { e } }$

Accepted Answer

A)  4 
B)  3 
C)  $\frac { 1 } { 4 }$ 
D)  5 
A)  4 
B)  3 
C)  $\frac { 1 } { 4 }$ 
D)  5

Question 19

Evaluate the logarithm.
-$\log _ { 8 } \frac { 1 } { 64 }$

Accepted Answer

A)  2 
B)  8 
C)  $- 8$ 
D)  $- 2$ 
A)  2 
B)  8 
C)  $- 8$ 
D)  $- 2$

Question 20

Decide whether the given functions are inverses.
-

Accepted Answer

A) True 
 B)False

Use properties of logarithms to evaluate the expression. - $1000 ^ { \log _ { 10 } 8 }$

Find the value. Give an approximation to four decimal places. - $\log \left( \frac { 637 } { 368 } \right)$

Round to the nearest thousandth. - $4 ^ { ( x + 3 ) } = 2 ^ { x }$

Find the value. Give an approximation to four decimal places. - $\log 298 + \log 17$

Write an equivalent expression in exponential form. - $\log _ { x } 25 = 2$

Which of the following is the same as $\log ( 12 x ) - \log ( 3 x )$ for $x > 0$ ?

Evaluate the logarithm. - $\log _ { 23 } 1$

Solve the equation. - $m ^ { - 4 } = \frac { 1 } { 81 }$

Write in logarithmic form. - $\left( \frac { 5 } { 6 } \right) ^ { 5 } = \frac { 3125 } { 7776 }$

Assume the cost of a gallon of milk is $3.40. With continuous compounding, find the time it would take the cost to be 4 times as much (to the nearest tenth of a year), at an annual inflation rate of 6%.

Use the properties of logarithms to rewrite the expression. Simplify the result if possible. Assume all variables represent positive real numbers. - $\log _ { 8 } \left( \frac { 4 \sqrt { 7 } } { 8 } \right)$ $\log _ { 8 } 4 + \frac { 1 } { 2 } \log _ { 8 } 7$

The decay of 243 mg of an isotope is given by $\mathrm { A } ( \mathrm { t } ) = 243 \mathrm { e } ^ { - 0.014 \mathrm { t } }$ where t is time in years since the initial amount of 243 mg was present. Find the amount (to the nearest milligram) left after 72 years.

Find the value. Give an approximation to four decimal places. - $\ln \sqrt [ 4 ] { \mathrm { e } }$

Evaluate the logarithm. - $\log _ { 8 } \frac { 1 } { 64 }$

Decide whether the given functions are inverses. -

Review of Basic Concepts

Equations and Inequalities

Graphs and Functions

Polynomials and Rational Functions

Systems and Matrices

Arithmetic Sequence: Common Difference and First n Terms

Filters

Exam 5: Inverse, Exponential, and Logarithmic Functions

Use properties of logarithms to evaluate the expression. - 1000log⁡1081000 ^ { \log _ { 10 } 8 }1000log10​8

Find the value. Give an approximation to four decimal places. - log⁡(637368)\log \left( \frac { 637 } { 368 } \right)log(368637​)

Round to the nearest thousandth. - 4(x+3)=2x4 ^ { ( x + 3 ) } = 2 ^ { x }4(x+3)=2x

Find the value. Give an approximation to four decimal places. - log⁡298+log⁡17\log 298 + \log 17log298+log17

Write an equivalent expression in exponential form. - log⁡x25=2\log _ { x } 25 = 2logx​25=2

Which of the following is the same as log⁡(12x)−log⁡(3x)\log ( 12 x ) - \log ( 3 x )log(12x)−log(3x) for x>0x > 0x>0 ?

Provide an appropriate response. -The graph of an exponential function with base a is given. Sketch the graph of h(x)=a−xh ( x ) = a - xh(x)=a−x . Give the domain and range of hhh . f(x)=axf ( x ) = a ^ { x }f(x)=ax

Evaluate the logarithm. - log⁡231\log _ { 23 } 1log23​1

Solve the equation. - m−4=181m ^ { - 4 } = \frac { 1 } { 81 }m−4=811​

Write in logarithmic form. - (56)5=31257776\left( \frac { 5 } { 6 } \right) ^ { 5 } = \frac { 3125 } { 7776 }(65​)5=77763125​

Assume the cost of a gallon of milk is $3.40. With continuous compounding, find the time it would take the cost to be 4 times as much (to the nearest tenth of a year), at an annual inflation rate of 6%.

The decay of 243 mg of an isotope is given by A(t)=243e−0.014t\mathrm { A } ( \mathrm { t } ) = 243 \mathrm { e } ^ { - 0.014 \mathrm { t } }A(t)=243e−0.014t where t is time in years since the initial amount of 243 mg was present. Find the amount (to the nearest milligram) left after 72 years.

Find the value. Give an approximation to four decimal places. - ln⁡e4\ln \sqrt [ 4 ] { \mathrm { e } }ln4e​

Evaluate the logarithm. - log⁡8164\log _ { 8 } \frac { 1 } { 64 }log8​641​

Decide whether the given functions are inverses. -

Review of Basic Concepts

Equations and Inequalities

Graphs and Functions

Polynomials and Rational Functions

Systems and Matrices

Arithmetic Sequence: Common Difference and First n Terms

Filters

Use properties of logarithms to evaluate the expression. - $1000 ^ { \log _ { 10 } 8 }$

Find the value. Give an approximation to four decimal places. - $\log \left( \frac { 637 } { 368 } \right)$

Round to the nearest thousandth. - $4 ^ { ( x + 3 ) } = 2 ^ { x }$

Find the value. Give an approximation to four decimal places. - $\log 298 + \log 17$

Write an equivalent expression in exponential form. - $\log _ { x } 25 = 2$

Which of the following is the same as $\log ( 12 x ) - \log ( 3 x )$ for $x > 0$ ?

Evaluate the logarithm. - $\log _ { 23 } 1$

Solve the equation. - $m ^ { - 4 } = \frac { 1 } { 81 }$

Write in logarithmic form. - $\left( \frac { 5 } { 6 } \right) ^ { 5 } = \frac { 3125 } { 7776 }$

The decay of 243 mg of an isotope is given by $\mathrm { A } ( \mathrm { t } ) = 243 \mathrm { e } ^ { - 0.014 \mathrm { t } }$ where t is time in years since the initial amount of 243 mg was present. Find the amount (to the nearest milligram) left after 72 years.

Find the value. Give an approximation to four decimal places. - $\ln \sqrt [ 4 ] { \mathrm { e } }$

Evaluate the logarithm. - $\log _ { 8 } \frac { 1 } { 64 }$