Exam 5: Exponential and Logarithmic Functions and Equations

Solve the problem. -Instruments on a satellite measure the amount of power generated by the satellite's power supply. The time t and the power P can be modeled by the funct $P = 50 e ^ { - t / 300 }$ , where t is in days and P is in watts. How much power will be available after 378 days? Round to the nearest hundredth.

(Multiple Choice)

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Question 121

Solve the equation. - $\log ( 5 x ) = \log 3 + \log ( x - 1 )$

(Multiple Choice)

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Question 122

Solve the problem. -A thermometer reading 73°F is placed inside a cold storage room with a constant temperature of 33°F. If the thermometer reads 68°F in 7 minutes, how long before it reaches 60°F? Round your answer to the nearest whole minute.

(Multiple Choice)

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Question 123

Solve the problem. - $f ( t ) = \frac { 560 } { 1 + 17.7 e ^ { - 0.19 t } }$ after they are introduced to a non-threatening habitat. How many butterflies are expected in the habitat after 15 months?

(Multiple Choice)

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Question 124

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. - $\left. \log _ { a } q - \log _ { a } r \right) + 5 \log _ { a } p$

(Multiple Choice)

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Question 125

Solve the exponential equation. Use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. - $2 ^ { 8 x } = 4$

(Multiple Choice)

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Question 126

Solve the equation. - $\frac { 1 } { 3 } \log _ { 2 } ( x + 6 ) = \log _ { 8 } ( 3 x )$

(Multiple Choice)

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Question 127

Use the change of base formula and a calculator to evaluate the logarithm. Round your answer to two decimal places. - $\log _ { 3 } 25$

(Multiple Choice)

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Question 128

Solve the equation. - $2 ^{( 5 - 3 x )} = \frac { 1 } { 16 }$

(Multiple Choice)

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Question 129

Graph the function. - $f ( x ) = \log _ { 3 } ( x - 1 )$ $Graph the function. - f ( x ) = \log _ { 3 } ( x - 1 )$

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Question 130

Solve the problem. -The rabbit population in a forest area grows at the rate of 7% monthly. If there are 270 rabbits in September, find how many rabbits (rounded to the nearest whole number)should be expected by next September. Use $\mathrm { v } = 270 ( 2.7 ) ^ { 0.07 \mathrm { t } }$

(Multiple Choice)

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Question 131

Use transformations to graph the function. - $f(x)=2-e^{-x}$ $Use transformations to graph the function. - f(x)=2-e^{-x}$

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Question 132

Solve the problem. -How long will it take for an investment to triple in value if it earns 11.5% compounded continuously? Round your answer to three decimal places.

(Multiple Choice)

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Question 133

Evaluate the logarithm without the use of a calculator. - $\log _ { 1 / 5 } 625$

(Multiple Choice)

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Question 134

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

(Multiple Choice)

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Question 135

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - $\log \frac { 6 x ^ { 5 } \sqrt [ 3 ] { 2 - x } } { 5 ( x + 2 ) ^ { 2 } }$

(Multiple Choice)

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Question 136

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. - $\log _ { 5 } 250 - \log _ { 5 } 2$

(Multiple Choice)

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Question 137

Write the logarithmic equation as an exponential equation. - $\log B = C$

(Multiple Choice)

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Question 138

Use the change of base formula and a calculator to evaluate the logarithm. Round your answer to two decimal places. - $\log _ { 2 / 3 } 19$

(Multiple Choice)

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Question 139

Find the domain of the function. - $f ( x ) = \ln \left( \frac { 1 } { x - 3 } \right)$

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Question 140

Solve the equation. - $\log ( 5 x ) = \log 3 + \log ( x - 1 )$

Solve the problem. -A thermometer reading 73°F is placed inside a cold storage room with a constant temperature of 33°F. If the thermometer reads 68°F in 7 minutes, how long before it reaches 60°F? Round your answer to the nearest whole minute.

Solve the problem. - $f ( t ) = \frac { 560 } { 1 + 17.7 e ^ { - 0.19 t } }$ after they are introduced to a non-threatening habitat. How many butterflies are expected in the habitat after 15 months?

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. - $\left. \log _ { a } q - \log _ { a } r \right) + 5 \log _ { a } p$

Solve the exponential equation. Use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. - $2 ^ { 8 x } = 4$

Solve the equation. - $\frac { 1 } { 3 } \log _ { 2 } ( x + 6 ) = \log _ { 8 } ( 3 x )$

Use the change of base formula and a calculator to evaluate the logarithm. Round your answer to two decimal places. - $\log _ { 3 } 25$

Solve the equation. - $2 ^{( 5 - 3 x )} = \frac { 1 } { 16 }$

Graph the function. - $f ( x ) = \log _ { 3 } ( x - 1 )$ $Graph the function. - f ( x ) = \log _ { 3 } ( x - 1 )$

Solve the problem. -The rabbit population in a forest area grows at the rate of 7% monthly. If there are 270 rabbits in September, find how many rabbits (rounded to the nearest whole number)should be expected by next September. Use $\mathrm { v } = 270 ( 2.7 ) ^ { 0.07 \mathrm { t } }$

Use transformations to graph the function. - $f(x)=2-e^{-x}$ $Use transformations to graph the function. - f(x)=2-e^{-x}$

Solve the problem. -How long will it take for an investment to triple in value if it earns 11.5% compounded continuously? Round your answer to three decimal places.

Evaluate the logarithm without the use of a calculator. - $\log _ { 1 / 5 } 625$

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

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - $\log \frac { 6 x ^ { 5 } \sqrt [ 3 ] { 2 - x } } { 5 ( x + 2 ) ^ { 2 } }$

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. - $\log _ { 5 } 250 - \log _ { 5 } 2$

Write the logarithmic equation as an exponential equation. - $\log B = C$

Use the change of base formula and a calculator to evaluate the logarithm. Round your answer to two decimal places. - $\log _ { 2 / 3 } 19$

Find the domain of the function. - $f ( x ) = \ln \left( \frac { 1 } { x - 3 } \right)$

Equations, Inequalities, and Applications

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Polynomial and Rational Functions

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Exam 5: Exponential and Logarithmic Functions and Equations

Solve the equation. - log⁡(5x)=log⁡3+log⁡(x−1)\log ( 5 x ) = \log 3 + \log ( x - 1 )log(5x)=log3+log(x−1)

Solve the problem. -A thermometer reading 73°F is placed inside a cold storage room with a constant temperature of 33°F. If the thermometer reads 68°F in 7 minutes, how long before it reaches 60°F? Round your answer to the nearest whole minute.

Solve the problem. - f(t)=5601+17.7e−0.19tf ( t ) = \frac { 560 } { 1 + 17.7 e ^ { - 0.19 t } }f(t)=1+17.7e−0.19t560​ after they are introduced to a non-threatening habitat. How many butterflies are expected in the habitat after 15 months?

Solve the exponential equation. Use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. - 28x=42 ^ { 8 x } = 428x=4

Solve the equation. - 13log⁡2(x+6)=log⁡8(3x)\frac { 1 } { 3 } \log _ { 2 } ( x + 6 ) = \log _ { 8 } ( 3 x )31​log2​(x+6)=log8​(3x)

Use the change of base formula and a calculator to evaluate the logarithm. Round your answer to two decimal places. - log⁡325\log _ { 3 } 25log3​25

Solve the equation. - 2(5−3x)=1162 ^{( 5 - 3 x )} = \frac { 1 } { 16 }2(5−3x)=161​

Graph the function. - f(x)=log⁡3(x−1)f ( x ) = \log _ { 3 } ( x - 1 )f(x)=log3​(x−1)

Use transformations to graph the function. - f(x)=2−e−xf(x)=2-e^{-x}f(x)=2−e−x

Solve the problem. -How long will it take for an investment to triple in value if it earns 11.5% compounded continuously? Round your answer to three decimal places.

Evaluate the logarithm without the use of a calculator. - log⁡1/5625\log _ { 1 / 5 } 625log1/5​625

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - log⁡7(7x)\log _ { 7 } ( 7 x )log7​(7x)

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - log⁡6x52−x35(x+2)2\log \frac { 6 x ^ { 5 } \sqrt [ 3 ] { 2 - x } } { 5 ( x + 2 ) ^ { 2 } }log5(x+2)26x532−x​​

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⁡5250−log⁡52\log _ { 5 } 250 - \log _ { 5 } 2log5​250−log5​2

Write the logarithmic equation as an exponential equation. - log⁡B=C\log B = ClogB=C

Use the change of base formula and a calculator to evaluate the logarithm. Round your answer to two decimal places. - log⁡2/319\log _ { 2 / 3 } 19log2/3​19

Find the domain of the function. - f(x)=ln⁡(1x−3)f ( x ) = \ln \left( \frac { 1 } { x - 3 } \right)f(x)=ln(x−31​)

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

Solve the equation. - $\log ( 5 x ) = \log 3 + \log ( x - 1 )$

Solve the problem. - $f ( t ) = \frac { 560 } { 1 + 17.7 e ^ { - 0.19 t } }$ after they are introduced to a non-threatening habitat. How many butterflies are expected in the habitat after 15 months?

Solve the exponential equation. Use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. - $2 ^ { 8 x } = 4$

Solve the equation. - $\frac { 1 } { 3 } \log _ { 2 } ( x + 6 ) = \log _ { 8 } ( 3 x )$

Use the change of base formula and a calculator to evaluate the logarithm. Round your answer to two decimal places. - $\log _ { 3 } 25$

Solve the equation. - $2 ^{( 5 - 3 x )} = \frac { 1 } { 16 }$

Graph the function. - $f ( x ) = \log _ { 3 } ( x - 1 )$ $Graph the function. - f ( x ) = \log _ { 3 } ( x - 1 )$

Use transformations to graph the function. - $f(x)=2-e^{-x}$ $Use transformations to graph the function. - f(x)=2-e^{-x}$

Evaluate the logarithm without the use of a calculator. - $\log _ { 1 / 5 } 625$

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

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - $\log \frac { 6 x ^ { 5 } \sqrt [ 3 ] { 2 - x } } { 5 ( x + 2 ) ^ { 2 } }$

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. - $\log _ { 5 } 250 - \log _ { 5 } 2$

Write the logarithmic equation as an exponential equation. - $\log B = C$

Use the change of base formula and a calculator to evaluate the logarithm. Round your answer to two decimal places. - $\log _ { 2 / 3 } 19$

Find the domain of the function. - $f ( x ) = \ln \left( \frac { 1 } { x - 3 } \right)$