Exam 4: Exponential and Logarithmic Functions

Use the quotient property of logarithms to write the logarithm as a difference of logarithms. Then simplify if possible. - $\log \left( \frac { m ^ { 4 } + n } { 1,000 } \right)$

(Multiple Choice)

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Question 121

Determine if the statement is true or false. - $\log e = \frac { 1 } { \ln 10 }$

(True/False)

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Question 122

Choose the one alternative that best completes the statement or answers the question. Solve for the indicated variable. - $\ln \left( \frac { k } { A } \right) = \frac { - E } { R T }$ for $k$

(Multiple Choice)

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Question 123

The graph of a function is given. Graph the inverse function. -

(Multiple Choice)

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Question 124

Use the change-of-base and a calculator to approximate the logarithm to 4 decimal places. - $\log _ { 8 } \left( 7.32 \cdot 10 ^ { - 7 } \right)$

(Multiple Choice)

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Question 125

Write the word or phrase that best completes each statement or answers the question. - $\log _ { 8 } \frac { 1 } { 512 } = - 3$

(Multiple Choice)

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Question 126

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

(Multiple Choice)

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Question 127

Write the logarithm as a sum or difference of logarithms. Simplify each term as much as possible. - $\log _ { 2 } \frac { p ^ { 5 } } { q ^ { 9 } }$

(Multiple Choice)

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Question 128

ng, in -The population of bacteria culture was 2000 at noon, and was increasing at a rate of $10 \%$ per hour. The number can be found using the function $P ( t ) = 2,000 ( 1.1 ) ^ { t }$ where $t$ is the number of hours past noon. Predict the population 11 hours later, at $11 \mathrm { PM }$ to the nearest whole number.

(Multiple Choice)

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Question 129

A one-to-one function is given. Write an expression for the inverse function. - $m ( x ) = 7 x ^ { 3 } + 2$

(Multiple Choice)

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Question 130

Find an equation for the inverse function. - $f ( x ) = \log ( x + 5 ) + 4$

(Multiple Choice)

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Question 131

The graph of a function is given. Graph the inverse function. -

(Multiple Choice)

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Question 132

A one-to-one function is given. Write an expression for the inverse function. - $f ( x ) = \sqrt [ 3 ] { x + 7 }$

(Multiple Choice)

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Question 133

Write the logarithmic expression as a single logarithm with coefficient 1, and simplify as much as possible. - $\frac { 1 } { 2 } \log _ { 2 } p + 4 \log _ { 2 } 3$

(Multiple Choice)

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Question 134

Write the logarithmic expression as a single logarithm with coefficient 1, and simplify as much as possible. - $\frac { 1 } { 2 } [ 6 \ln ( x - 3 ) + \ln x - 2 \ln x ]$

(Multiple Choice)

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Question 135

Graph the function and write the domain and range in interval notation. - $f ( x ) = \left( \frac { 3 } { 2 } \right) ^ { x }$

(Multiple Choice)

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Question 136

Simplify the expression. - $3 ^ { \log _ { 3 } ( 4 x + 4 y ) }$

(Multiple Choice)

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Question 137

Choose the one alternative that best completes the statement or answers the question. Solve for the indicated variable. - $A = P ( 1 + r ) ^ { t }$ for $\mathrm { t }$

(Multiple Choice)

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Question 138

Solve the problem. -A $\$ 3,000$ bond grows to $\$ 4,475.47$ in 8 yr under continuous compounding. Find the interest rate. Round our answer to the nearest whole percent.

(Multiple Choice)

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Question 139

Simplify the expression. - $\log _ { 7 } \left( \frac { 1 } { 49 } \right)$

(Multiple Choice)

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Question 140

Use the quotient property of logarithms to write the logarithm as a difference of logarithms. Then simplify if possible. - $\log \left( \frac { m ^ { 4 } + n } { 1,000 } \right)$

Determine if the statement is true or false. - $\log e = \frac { 1 } { \ln 10 }$

Choose the one alternative that best completes the statement or answers the question. Solve for the indicated variable. - $\ln \left( \frac { k } { A } \right) = \frac { - E } { R T }$ for $k$

The graph of a function is given. Graph the inverse function. -

Use the change-of-base and a calculator to approximate the logarithm to 4 decimal places. - $\log _ { 8 } \left( 7.32 \cdot 10 ^ { - 7 } \right)$

Write the word or phrase that best completes each statement or answers the question. - $\log _ { 8 } \frac { 1 } { 512 } = - 3$

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

Write the logarithm as a sum or difference of logarithms. Simplify each term as much as possible. - $\log _ { 2 } \frac { p ^ { 5 } } { q ^ { 9 } }$

A one-to-one function is given. Write an expression for the inverse function. - $m ( x ) = 7 x ^ { 3 } + 2$

Find an equation for the inverse function. - $f ( x ) = \log ( x + 5 ) + 4$

The graph of a function is given. Graph the inverse function. -

A one-to-one function is given. Write an expression for the inverse function. - $f ( x ) = \sqrt [ 3 ] { x + 7 }$

Write the logarithmic expression as a single logarithm with coefficient 1, and simplify as much as possible. - $\frac { 1 } { 2 } \log _ { 2 } p + 4 \log _ { 2 } 3$

Write the logarithmic expression as a single logarithm with coefficient 1, and simplify as much as possible. - $\frac { 1 } { 2 } [ 6 \ln ( x - 3 ) + \ln x - 2 \ln x ]$

Graph the function and write the domain and range in interval notation. - $f ( x ) = \left( \frac { 3 } { 2 } \right) ^ { x }$

Simplify the expression. - $3 ^ { \log _ { 3 } ( 4 x + 4 y ) }$

Choose the one alternative that best completes the statement or answers the question. Solve for the indicated variable. - $A = P ( 1 + r ) ^ { t }$ for $\mathrm { t }$

Solve the problem. -A $\$ 3,000$ bond grows to $\$ 4,475.47$ in 8 yr under continuous compounding. Find the interest rate. Round our answer to the nearest whole percent.

Simplify the expression. - $\log _ { 7 } \left( \frac { 1 } { 49 } \right)$

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Exam 4: Exponential and Logarithmic Functions

Use the quotient property of logarithms to write the logarithm as a difference of logarithms. Then simplify if possible. - log⁡(m4+n1,000)\log \left( \frac { m ^ { 4 } + n } { 1,000 } \right)log(1,000m4+n​)

Determine if the statement is true or false. - log⁡e=1ln⁡10\log e = \frac { 1 } { \ln 10 }loge=ln101​

Choose the one alternative that best completes the statement or answers the question. Solve for the indicated variable. - ln⁡(kA)=−ERT\ln \left( \frac { k } { A } \right) = \frac { - E } { R T }ln(Ak​)=RT−E​ for kkk

The graph of a function is given. Graph the inverse function. -

Use the change-of-base and a calculator to approximate the logarithm to 4 decimal places. - log⁡8(7.32⋅10−7)\log _ { 8 } \left( 7.32 \cdot 10 ^ { - 7 } \right)log8​(7.32⋅10−7)

Write the word or phrase that best completes each statement or answers the question. - log⁡81512=−3\log _ { 8 } \frac { 1 } { 512 } = - 3log8​5121​=−3

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

Write the logarithm as a sum or difference of logarithms. Simplify each term as much as possible. - log⁡2p5q9\log _ { 2 } \frac { p ^ { 5 } } { q ^ { 9 } }log2​q9p5​

A one-to-one function is given. Write an expression for the inverse function. - m(x)=7x3+2m ( x ) = 7 x ^ { 3 } + 2m(x)=7x3+2

Find an equation for the inverse function. - f(x)=log⁡(x+5)+4f ( x ) = \log ( x + 5 ) + 4f(x)=log(x+5)+4

The graph of a function is given. Graph the inverse function. -

A one-to-one function is given. Write an expression for the inverse function. - f(x)=x+73f ( x ) = \sqrt [ 3 ] { x + 7 }f(x)=3x+7​

Write the logarithmic expression as a single logarithm with coefficient 1, and simplify as much as possible. - 12log⁡2p+4log⁡23\frac { 1 } { 2 } \log _ { 2 } p + 4 \log _ { 2 } 321​log2​p+4log2​3

Write the logarithmic expression as a single logarithm with coefficient 1, and simplify as much as possible. - 12[6ln⁡(x−3)+ln⁡x−2ln⁡x]\frac { 1 } { 2 } [ 6 \ln ( x - 3 ) + \ln x - 2 \ln x ]21​[6ln(x−3)+lnx−2lnx]

Graph the function and write the domain and range in interval notation. - f(x)=(32)xf ( x ) = \left( \frac { 3 } { 2 } \right) ^ { x }f(x)=(23​)x

Simplify the expression. - 3log⁡3(4x+4y)3 ^ { \log _ { 3 } ( 4 x + 4 y ) }3log3​(4x+4y)

Choose the one alternative that best completes the statement or answers the question. Solve for the indicated variable. - A=P(1+r)tA = P ( 1 + r ) ^ { t }A=P(1+r)t for t\mathrm { t }t

Solve the problem. -A $3,000\$ 3,000$3,000 bond grows to $4,475.47\$ 4,475.47$4,475.47 in 8 yr under continuous compounding. Find the interest rate. Round our answer to the nearest whole percent.

Simplify the expression. - log⁡7(149)\log _ { 7 } \left( \frac { 1 } { 49 } \right)log7​(491​)

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

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Use the quotient property of logarithms to write the logarithm as a difference of logarithms. Then simplify if possible. - $\log \left( \frac { m ^ { 4 } + n } { 1,000 } \right)$

Determine if the statement is true or false. - $\log e = \frac { 1 } { \ln 10 }$

Choose the one alternative that best completes the statement or answers the question. Solve for the indicated variable. - $\ln \left( \frac { k } { A } \right) = \frac { - E } { R T }$ for $k$

Use the change-of-base and a calculator to approximate the logarithm to 4 decimal places. - $\log _ { 8 } \left( 7.32 \cdot 10 ^ { - 7 } \right)$

Write the word or phrase that best completes each statement or answers the question. - $\log _ { 8 } \frac { 1 } { 512 } = - 3$

Write the logarithm as a sum or difference of logarithms. Simplify each term as much as possible. - $\log _ { 2 } \frac { p ^ { 5 } } { q ^ { 9 } }$

A one-to-one function is given. Write an expression for the inverse function. - $m ( x ) = 7 x ^ { 3 } + 2$

Find an equation for the inverse function. - $f ( x ) = \log ( x + 5 ) + 4$

A one-to-one function is given. Write an expression for the inverse function. - $f ( x ) = \sqrt [ 3 ] { x + 7 }$

Write the logarithmic expression as a single logarithm with coefficient 1, and simplify as much as possible. - $\frac { 1 } { 2 } \log _ { 2 } p + 4 \log _ { 2 } 3$

Write the logarithmic expression as a single logarithm with coefficient 1, and simplify as much as possible. - $\frac { 1 } { 2 } [ 6 \ln ( x - 3 ) + \ln x - 2 \ln x ]$

Graph the function and write the domain and range in interval notation. - $f ( x ) = \left( \frac { 3 } { 2 } \right) ^ { x }$

Simplify the expression. - $3 ^ { \log _ { 3 } ( 4 x + 4 y ) }$

Choose the one alternative that best completes the statement or answers the question. Solve for the indicated variable. - $A = P ( 1 + r ) ^ { t }$ for $\mathrm { t }$

Solve the problem. -A $\$ 3,000$ bond grows to $\$ 4,475.47$ in 8 yr under continuous compounding. Find the interest rate. Round our answer to the nearest whole percent.

Simplify the expression. - $\log _ { 7 } \left( \frac { 1 } { 49 } \right)$