Exam 5: Exponential and Logarithmic Functions and Equations

Use properties of logarithms to condense the logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions. - $\log x + \log \left( x ^ { 2 } - 144 \right) - \log 7 - \log ( x - 12 )$

(Multiple Choice)

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Question 61

Use transformations to graph the function. - $f(x)=5(x-3)-2$

(Multiple Choice)

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Question 62

Write the logarithmic equation as an exponential equation. - $\log _ { 3 } 27 = x$

(Multiple Choice)

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Question 63

Solve the problem. - $P ( t ) = \frac { 170 } { 1 + 16 e ^ { - 0.188 t } }$ territory after t years. When will the population be 80?

(Multiple Choice)

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Question 64

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - $\log _ { 2 } \left( \frac { 7 } { 13 } \right)$

(Multiple Choice)

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Question 65

Evaluate the expression without the use of a calculator, and then verify your answer using a calculator. -ln $\mathrm { e } ^ { \sqrt { 2 } }$

(Multiple Choice)

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Question 66

Solve the problem. -Conservationists tagged 50 black-nosed rabbits in a national forest in 1990. In 1991, they tagged 100 black-nosed rabbits in the same range. If the rabbit population follows the exponential law, how many rabbits will be in the range 4 years from 1990?

(Multiple Choice)

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Question 67

Solve the problem. -The amount of a radioactive substance present, in grams, at time t in months is given by the formula y = 8000(2)-0.3t. Find the number of grams present in 2 years. If necessary, round to three decimal places.

(Multiple Choice)

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Question 68

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - $\ln \sqrt [ 6 ] { x }$

(Multiple Choice)

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Question 69

Use transformations to graph the function. - $f(x)=e^{x}+5$ $Use transformations to graph the function. - f(x)=e^{x}+5$

(Multiple Choice)

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Question 70

Solve the logarithmic equation. - $\log _ { 2 } x = \log _{\sqrt { 2 }} 7$

(Multiple Choice)

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Question 71

Use transformations to graph the function. Determine the domain, range, and horizontal asymptote of the function. - $f ( x ) = 2 ^{( x - 3 )}$ $Use transformations to graph the function. Determine the domain, range, and horizontal asymptote of the function. - f ( x ) = 2 ^{( x - 3 )}$

(Multiple Choice)

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Question 72

Use properties of logarithms to condense the logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions. - $2 \log _ { y } 3 + \log _ { y } 2$

(Multiple Choice)

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Question 73

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - $\log _ { W } \frac { 11 x } { 5 }$

(Multiple Choice)

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Question 74

Graph the function. - $f ( x ) = \log 1 / 4 x$ $Graph the function. - f ( x ) = \log 1 / 4 x$

(Multiple Choice)

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Question 75

Graph the function. -

(Multiple Choice)

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Question 76

Solve the problem. -An initial investment of $1740 is appreciated for 14 years in an account that earns 7% interest, compounded continuously. Find the amount of money in the account at the end of the period. Round to the nearest cent.

(Multiple Choice)

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Question 77

Write the exponential equation as an equation involving a common logarithm or a natural logarithm. - $\mathrm { e } ^ { - 3 } = \mathrm { t }$

(Multiple Choice)

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Question 78

Solve the problem. -If Emery has $1100 to invest at 6% per year compounded monthly, how long will it be before he has $2100? If the compounding is continuous, how long will it be? (Round your answers to three decimal places.)

(Multiple Choice)

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Question 79

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - $\log _ { 3 } \frac { \sqrt { x } } { 9 }$

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Question 80

Showing 61 - 80 of 186

Use properties of logarithms to condense the logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions. - $\log x + \log \left( x ^ { 2 } - 144 \right) - \log 7 - \log ( x - 12 )$

Use transformations to graph the function. - $f(x)=5(x-3)-2$

Write the logarithmic equation as an exponential equation. - $\log _ { 3 } 27 = x$

Solve the problem. - $P ( t ) = \frac { 170 } { 1 + 16 e ^ { - 0.188 t } }$ territory after t years. When will the population be 80?

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - $\log _ { 2 } \left( \frac { 7 } { 13 } \right)$

Evaluate the expression without the use of a calculator, and then verify your answer using a calculator. -ln $\mathrm { e } ^ { \sqrt { 2 } }$

Solve the problem. -Conservationists tagged 50 black-nosed rabbits in a national forest in 1990. In 1991, they tagged 100 black-nosed rabbits in the same range. If the rabbit population follows the exponential law, how many rabbits will be in the range 4 years from 1990?

Solve the problem. -The amount of a radioactive substance present, in grams, at time t in months is given by the formula y = 8000(2)-0.3t. Find the number of grams present in 2 years. If necessary, round to three decimal places.

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - $\ln \sqrt [ 6 ] { x }$

Use transformations to graph the function. - $f(x)=e^{x}+5$ $Use transformations to graph the function. - f(x)=e^{x}+5$

Solve the logarithmic equation. - $\log _ { 2 } x = \log _{\sqrt { 2 }} 7$

Use transformations to graph the function. Determine the domain, range, and horizontal asymptote of the function. - $f ( x ) = 2 ^{( x - 3 )}$ $Use transformations to graph the function. Determine the domain, range, and horizontal asymptote of the function. - f ( x ) = 2 ^{( x - 3 )}$

Use properties of logarithms to condense the logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions. - $2 \log _ { y } 3 + \log _ { y } 2$

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - $\log _ { W } \frac { 11 x } { 5 }$

Graph the function. - $f ( x ) = \log 1 / 4 x$ $Graph the function. - f ( x ) = \log 1 / 4 x$

Graph the function. -

Solve the problem. -An initial investment of $1740 is appreciated for 14 years in an account that earns 7% interest, compounded continuously. Find the amount of money in the account at the end of the period. Round to the nearest cent.

Write the exponential equation as an equation involving a common logarithm or a natural logarithm. - $\mathrm { e } ^ { - 3 } = \mathrm { t }$

Solve the problem. -If Emery has $1100 to invest at 6% per year compounded monthly, how long will it be before he has $2100? If the compounding is continuous, how long will it be? (Round your answers to three decimal places.)

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - $\log _ { 3 } \frac { \sqrt { x } } { 9 }$

Equations, Inequalities, and Applications

The Rectangular Coordinate System, Lines, and Circles

Functions

Polynomial and Rational Functions

Conic Sections

Systems of Equations and Inequalities

Matrices

Sequences and Series; Counting and Probability

Math Exercises: Sets, Intervals, Absolute Value, and Properties

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Exam 5: Exponential and Logarithmic Functions and Equations

Use transformations to graph the function. - f(x)=5(x−3)−2f(x)=5(x-3)-2f(x)=5(x−3)−2

Write the logarithmic equation as an exponential equation. - log⁡327=x\log _ { 3 } 27 = xlog3​27=x

Solve the problem. - P(t)=1701+16e−0.188tP ( t ) = \frac { 170 } { 1 + 16 e ^ { - 0.188 t } }P(t)=1+16e−0.188t170​ territory after t years. When will the population be 80?

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - log⁡2(713)\log _ { 2 } \left( \frac { 7 } { 13 } \right)log2​(137​)

Evaluate the expression without the use of a calculator, and then verify your answer using a calculator. -ln e2\mathrm { e } ^ { \sqrt { 2 } }e2​

Solve the problem. -Conservationists tagged 50 black-nosed rabbits in a national forest in 1990. In 1991, they tagged 100 black-nosed rabbits in the same range. If the rabbit population follows the exponential law, how many rabbits will be in the range 4 years from 1990?

Solve the problem. -The amount of a radioactive substance present, in grams, at time t in months is given by the formula y = 8000(2)-0.3t. Find the number of grams present in 2 years. If necessary, round to three decimal places.

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - ln⁡x6\ln \sqrt [ 6 ] { x }ln6x​

Use transformations to graph the function. - f(x)=ex+5f(x)=e^{x}+5f(x)=ex+5

Solve the logarithmic equation. - log⁡2x=log⁡27\log _ { 2 } x = \log _{\sqrt { 2 }} 7log2​x=log2​​7

Use transformations to graph the function. Determine the domain, range, and horizontal asymptote of the function. - f(x)=2(x−3)f ( x ) = 2 ^{( x - 3 )}f(x)=2(x−3)

Use properties of logarithms to condense the logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions. - 2log⁡y3+log⁡y22 \log _ { y } 3 + \log _ { y } 22logy​3+logy​2

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - log⁡W11x5\log _ { W } \frac { 11 x } { 5 }logW​511x​

Graph the function. - f(x)=log⁡1/4xf ( x ) = \log 1 / 4 xf(x)=log1/4x

Graph the function. -

Solve the problem. -An initial investment of $1740 is appreciated for 14 years in an account that earns 7% interest, compounded continuously. Find the amount of money in the account at the end of the period. Round to the nearest cent.

Write the exponential equation as an equation involving a common logarithm or a natural logarithm. - e−3=t\mathrm { e } ^ { - 3 } = \mathrm { t }e−3=t

Solve the problem. -If Emery has $1100 to invest at 6% per year compounded monthly, how long will it be before he has $2100? If the compounding is continuous, how long will it be? (Round your answers to three decimal places.)

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - log⁡3x9\log _ { 3 } \frac { \sqrt { x } } { 9 }log3​9x​​

Equations, Inequalities, and Applications

The Rectangular Coordinate System, Lines, and Circles

Functions

Polynomial and Rational Functions

Conic Sections

Systems of Equations and Inequalities

Matrices

Sequences and Series; Counting and Probability

Math Exercises: Sets, Intervals, Absolute Value, and Properties

Filters

Use transformations to graph the function. - $f(x)=5(x-3)-2$

Write the logarithmic equation as an exponential equation. - $\log _ { 3 } 27 = x$

Solve the problem. - $P ( t ) = \frac { 170 } { 1 + 16 e ^ { - 0.188 t } }$ territory after t years. When will the population be 80?

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - $\log _ { 2 } \left( \frac { 7 } { 13 } \right)$

Evaluate the expression without the use of a calculator, and then verify your answer using a calculator. -ln $\mathrm { e } ^ { \sqrt { 2 } }$

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - $\ln \sqrt [ 6 ] { x }$

Use transformations to graph the function. - $f(x)=e^{x}+5$ $Use transformations to graph the function. - f(x)=e^{x}+5$

Solve the logarithmic equation. - $\log _ { 2 } x = \log _{\sqrt { 2 }} 7$

Use transformations to graph the function. Determine the domain, range, and horizontal asymptote of the function. - $f ( x ) = 2 ^{( x - 3 )}$ $Use transformations to graph the function. Determine the domain, range, and horizontal asymptote of the function. - f ( x ) = 2 ^{( x - 3 )}$

Use properties of logarithms to condense the logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions. - $2 \log _ { y } 3 + \log _ { y } 2$

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - $\log _ { W } \frac { 11 x } { 5 }$

Graph the function. - $f ( x ) = \log 1 / 4 x$ $Graph the function. - f ( x ) = \log 1 / 4 x$

Write the exponential equation as an equation involving a common logarithm or a natural logarithm. - $\mathrm { e } ^ { - 3 } = \mathrm { t }$

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - $\log _ { 3 } \frac { \sqrt { x } } { 9 }$