Exam 4: Exponential and Logarithmic Functions

Choose the one alternative that best completes the statement or answers the question. Use the product property of logarithms to write the logarithm as a sum of logarithms. Then simplify if possible. - $\log _ { 2 } 8 x$

(Multiple Choice)

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Question 301

Choose the one alternative that best completes the statement or answers the question. Solve the equation. - $9 ^ { x } = \frac { 1 } { 729 }$

(Multiple Choice)

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Question 302

Write the logarithmic expression as a single logarithm with coefficient 1, and simplify as much as possible. - $\log _ { 5 } 5 + \log _ { 5 } 40 - \log _ { 5 } 8$

(Multiple Choice)

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Question 303

Solve the problem. -Suppose that $16,000 is invested in a bond fund and the account grows to $18,552.21 in 4 yr. Use the model $A = P e ^ { r t }$ to determine the average rate of return under continuous compounding. Round to The nearest tenth of a percent.

(Multiple Choice)

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Question 304

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -The equivalence property of exponential expressions indicates that if $b ^ { x } = b ^ { y }$ then = .

(Short Answer)

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Question 305

Solve the equation. Write the solution set with the exact solutions. Also give approximate solutions to 4 decimal places if necessary. - $\ln x + \ln ( x + 4 ) = \ln ( 2 x + 35 )$

(Multiple Choice)

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Question 306

Choose the one alternative that best completes the statement or answers the question. Use the product property of logarithms to write the logarithm as a sum of logarithms. Then simplify if possible. - $\log ( 10,000 y )$

(Multiple Choice)

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Question 307

Write the domain in interval notation. - $f ( x ) = \ln ( \sqrt { x + 5 } - 1 )$

(Multiple Choice)

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Question 308

a. Use transformations to graph the function. b. Write the domain and range in interval notation. c. Determine the vertical asymptote. - $y = \log _ { 5 } ( x + 3 )$

(Multiple Choice)

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Question 309

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -An equation containing a variable within a logarithmic expression is called a equation.

(Short Answer)

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Question 310

Choose the one alternative that best completes the statement or answers the question. Solve the equation. - $\sqrt [ 5 ] { 49 } = 7 ^ { t }$

(Multiple Choice)

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Question 311

Determine if the relation defines y as a one-to-one function of x. -

(Multiple Choice)

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Question 312

Solve the problem. -Use the graph of $y = \left( \frac { 1 } { 3 } \right) ^ { x }$ to graph the function. Write the domain and range in interval notation. $f ( x ) = - \left( \frac { 1 } { 3 } \right) ^ { x } + 2$

(Multiple Choice)

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Question 313

If no horizontal line intersects the graph of a function f in more than one point then f is a- - function.

(Short Answer)

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Question 314

Choose the one alternative that best completes the statement or answers the question. Use the product property of logarithms to write the logarithm as a sum of logarithms. Then simplify if possible. - $\log _ { 2 } 8 x$

Choose the one alternative that best completes the statement or answers the question. Solve the equation. - $9 ^ { x } = \frac { 1 } { 729 }$

Write the logarithmic expression as a single logarithm with coefficient 1, and simplify as much as possible. - $\log _ { 5 } 5 + \log _ { 5 } 40 - \log _ { 5 } 8$

Solve the problem. -Suppose that $16,000 is invested in a bond fund and the account grows to $18,552.21 in 4 yr. Use the model $A = P e ^ { r t }$ to determine the average rate of return under continuous compounding. Round to The nearest tenth of a percent.

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -The equivalence property of exponential expressions indicates that if $b ^ { x } = b ^ { y }$ then = .

Solve the equation. Write the solution set with the exact solutions. Also give approximate solutions to 4 decimal places if necessary. - $\ln x + \ln ( x + 4 ) = \ln ( 2 x + 35 )$

Choose the one alternative that best completes the statement or answers the question. Use the product property of logarithms to write the logarithm as a sum of logarithms. Then simplify if possible. - $\log ( 10,000 y )$

Write the domain in interval notation. - $f ( x ) = \ln ( \sqrt { x + 5 } - 1 )$

a. Use transformations to graph the function. b. Write the domain and range in interval notation. c. Determine the vertical asymptote. - $y = \log _ { 5 } ( x + 3 )$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -An equation containing a variable within a logarithmic expression is called a equation.

Choose the one alternative that best completes the statement or answers the question. Solve the equation. - $\sqrt [ 5 ] { 49 } = 7 ^ { t }$

Determine if the relation defines y as a one-to-one function of x. -

Solve the problem. -Use the graph of $y = \left( \frac { 1 } { 3 } \right) ^ { x }$ to graph the function. Write the domain and range in interval notation. $f ( x ) = - \left( \frac { 1 } { 3 } \right) ^ { x } + 2$

If no horizontal line intersects the graph of a function f in more than one point then f is a- - function.

Equations and Inequalities

Functions and Relations

Polynomial and Rational Functions

Systems of Equations and Inequalities

Matrices and Determinants and Applications

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Exam 4: Exponential and Logarithmic Functions

Choose the one alternative that best completes the statement or answers the question. Use the product property of logarithms to write the logarithm as a sum of logarithms. Then simplify if possible. - log⁡28x\log _ { 2 } 8 xlog2​8x

Choose the one alternative that best completes the statement or answers the question. Solve the equation. - 9x=17299 ^ { x } = \frac { 1 } { 729 }9x=7291​

Write the logarithmic expression as a single logarithm with coefficient 1, and simplify as much as possible. - log⁡55+log⁡540−log⁡58\log _ { 5 } 5 + \log _ { 5 } 40 - \log _ { 5 } 8log5​5+log5​40−log5​8

Solve the problem. -Suppose that $16,000 is invested in a bond fund and the account grows to $18,552.21 in 4 yr. Use the model A=PertA = P e ^ { r t }A=Pert to determine the average rate of return under continuous compounding. Round to The nearest tenth of a percent.

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -The equivalence property of exponential expressions indicates that if bx=byb ^ { x } = b ^ { y }bx=by then = .

Solve the equation. Write the solution set with the exact solutions. Also give approximate solutions to 4 decimal places if necessary. - ln⁡x+ln⁡(x+4)=ln⁡(2x+35)\ln x + \ln ( x + 4 ) = \ln ( 2 x + 35 )lnx+ln(x+4)=ln(2x+35)

Choose the one alternative that best completes the statement or answers the question. Use the product property of logarithms to write the logarithm as a sum of logarithms. Then simplify if possible. - log⁡(10,000y)\log ( 10,000 y )log(10,000y)

Write the domain in interval notation. - f(x)=ln⁡(x+5−1)f ( x ) = \ln ( \sqrt { x + 5 } - 1 )f(x)=ln(x+5​−1)

a. Use transformations to graph the function. b. Write the domain and range in interval notation. c. Determine the vertical asymptote. - y=log⁡5(x+3)y = \log _ { 5 } ( x + 3 )y=log5​(x+3)

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -An equation containing a variable within a logarithmic expression is called a equation.

Choose the one alternative that best completes the statement or answers the question. Solve the equation. - 495=7t\sqrt [ 5 ] { 49 } = 7 ^ { t }549​=7t

Determine if the relation defines y as a one-to-one function of x. -

Solve the problem. -Use the graph of y=(13)xy = \left( \frac { 1 } { 3 } \right) ^ { x }y=(31​)x to graph the function. Write the domain and range in interval notation. f(x)=−(13)x+2f ( x ) = - \left( \frac { 1 } { 3 } \right) ^ { x } + 2f(x)=−(31​)x+2

If no horizontal line intersects the graph of a function f in more than one point then f is a________-________ -________ function.

Equations and Inequalities

Functions and Relations

Polynomial and Rational Functions

Systems of Equations and Inequalities

Matrices and Determinants and Applications

Analytic Geometry

Sequences, Series, Induction, and Probability

Review of Prerequisites

Filters

Choose the one alternative that best completes the statement or answers the question. Use the product property of logarithms to write the logarithm as a sum of logarithms. Then simplify if possible. - $\log _ { 2 } 8 x$

Choose the one alternative that best completes the statement or answers the question. Solve the equation. - $9 ^ { x } = \frac { 1 } { 729 }$

Write the logarithmic expression as a single logarithm with coefficient 1, and simplify as much as possible. - $\log _ { 5 } 5 + \log _ { 5 } 40 - \log _ { 5 } 8$

Solve the problem. -Suppose that $16,000 is invested in a bond fund and the account grows to $18,552.21 in 4 yr. Use the model $A = P e ^ { r t }$ to determine the average rate of return under continuous compounding. Round to The nearest tenth of a percent.

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -The equivalence property of exponential expressions indicates that if $b ^ { x } = b ^ { y }$ then = .

Solve the equation. Write the solution set with the exact solutions. Also give approximate solutions to 4 decimal places if necessary. - $\ln x + \ln ( x + 4 ) = \ln ( 2 x + 35 )$

Choose the one alternative that best completes the statement or answers the question. Use the product property of logarithms to write the logarithm as a sum of logarithms. Then simplify if possible. - $\log ( 10,000 y )$

Write the domain in interval notation. - $f ( x ) = \ln ( \sqrt { x + 5 } - 1 )$

a. Use transformations to graph the function. b. Write the domain and range in interval notation. c. Determine the vertical asymptote. - $y = \log _ { 5 } ( x + 3 )$

Choose the one alternative that best completes the statement or answers the question. Solve the equation. - $\sqrt [ 5 ] { 49 } = 7 ^ { t }$

Solve the problem. -Use the graph of $y = \left( \frac { 1 } { 3 } \right) ^ { x }$ to graph the function. Write the domain and range in interval notation. $f ( x ) = - \left( \frac { 1 } { 3 } \right) ^ { x } + 2$

If no horizontal line intersects the graph of a function f in more than one point then f is a- - function.