Question 1

Expand the logarithmic expression. $\ln \left( A B ^ { 2 } C ^ { 3 } \right)$

Accepted Answer

The answer of Expand the logarithmic expression. \(\ln \left( A...

Question 2

MaryAnna wants to invest $\$ 6,500$ at an interest rate of $7.5 \%$
Per year, compounded daily. How long will it take her investment to grow to $\$ 8,000 ?$

Accepted Answer

A)  $2.7 \text { years }$ 
B)  $27 \text { years }$ 
C)  $0.27 \text { years }$ 
D)  $37 \text { years }$ 
E)  $1 \text { year }$ 
A)  $2.7 \text { years }$ 
B)  $27 \text { years }$ 
C)  $0.27 \text { years }$ 
D)  $37 \text { years }$ 
E)  $1 \text { year }$

Question 3

Combine into a single logarithm. $\ln 2 + \ln ( x + 1 ) - \frac { 1 } { 3 } \ln ( 4 x + 7 )$

Accepted Answer

The answer of Combine into a single logarithm. \(\ln 2...

Question 4

Graph the function, not by plotting points, but by starting from the graph of $y = e ^ { x }$ . State the domain, range, and asymptote. $h ( x ) = e ^ { x + 1 } - 5$

Accepted Answer

Domain: @#LAT-DLM&

Question 5

Combine into a single logarithm. $\frac { 3 } { 2 } \ln ( x - y ) - 2 \ln \left( x ^ { 2 } + y ^ { 2 } \right)$

Accepted Answer

A)  $\ln \frac { ( x - y ) ^ { 3 } } { \left( x ^ { 2 } + y ^ { 2 } \right) ^ { 2 } }$ 
B)  $\ln \frac { \sqrt [ 3 ] { ( x - y ) ^ { 2 } } } { \left( x ^ { 2 } + y ^ { 2 } \right) ^ { 3 } }$ 
C)  $\ln \frac { \sqrt { ( x - y ) ^ { 3 } } } { \left( x ^ { 2 } - y ^ { 2 } \right) ^ { 2 } }$ 
D)  $\ln \frac { \sqrt [ 3 ] { ( x - y ) ^ { 2 } } } { \left( x ^ { 2 } + y ^ { 2 } \right) ^ { 2 } }$ 
E)  $\ln \frac { \sqrt { ( x - y ) ^ { 3 } } } { \left( x ^ { 2 } + y ^ { 2 } \right) ^ { 2 } }$ 
A)  $\ln \frac { ( x - y ) ^ { 3 } } { \left( x ^ { 2 } + y ^ { 2 } \right) ^ { 2 } }$ 
B)  $\ln \frac { \sqrt [ 3 ] { ( x - y ) ^ { 2 } } } { \left( x ^ { 2 } + y ^ { 2 } \right) ^ { 3 } }$ 
C)  $\ln \frac { \sqrt { ( x - y ) ^ { 3 } } } { \left( x ^ { 2 } - y ^ { 2 } \right) ^ { 2 } }$ 
D)  $\ln \frac { \sqrt [ 3 ] { ( x - y ) ^ { 2 } } } { \left( x ^ { 2 } + y ^ { 2 } \right) ^ { 2 } }$ 
E)  $\ln \frac { \sqrt { ( x - y ) ^ { 3 } } } { \left( x ^ { 2 } + y ^ { 2 } \right) ^ { 2 } }$

Question 6

Use the Change of Base Formula and a calculator to evaluate the logarithm, correct to six decimal places. Use either natural or common logarithms. $\log _ { 6 } 534$

Accepted Answer

A)  $0.001457$ 
B)  $37.682375$ 
C)  $6.280396$ 
D)  $2.727541$ 
E)  $3.505156$ 
A)  $0.001457$ 
B)  $37.682375$ 
C)  $6.280396$ 
D)  $2.727541$ 
E)  $3.505156$

Question 7

Find the domain, range, and asymptote of the function. $g ( x ) = 2 + \log _ { 2 } ( x + 4 )$

Accepted Answer

A)  Domain: $( - 4 , \infty )$
, Range: $( 2 , \infty )$
, Asymptote: $x = - 4$ 
B)  Domain: $( 4 , \infty )$
, Range: $( 4 , \infty )$
, Asymptote: $x = 4$ 
C)  Domain: $( - 4 , \infty )$
, Range: $(-\infty, \infty )$
, Asymptote: $x = - 4$ 
D)  Domain: $( - 4 , \infty )$
, Range: $( - 4 , \infty )$
, Asymptote: $x = 4$ 
E)  none of these 
A)  Domain: $( - 4 , \infty )$
, Range: $( 2 , \infty )$
, Asymptote: $x = - 4$ 
B)  Domain: $( 4 , \infty )$
, Range: $( 4 , \infty )$
, Asymptote: $x = 4$ 
C)  Domain: $( - 4 , \infty )$
, Range: $(-\infty, \infty )$
, Asymptote: $x = - 4$ 
D)  Domain: $( - 4 , \infty )$
, Range: $( - 4 , \infty )$
, Asymptote: $x = 4$ 
E)  none of these

Question 8

Sketch the graph of the function. $f ( x ) = 3 + 3 ^ { - x }$

Accepted Answer

A)   
B)   
C)   
D)   
A)   
B)   
C)   
D)

Question 9

Use a graphing device to find the solutions of the equation, correct to two decimal places. $3 \ln x = 6 - 2 x$

Accepted Answer

The answer of Use a graphing device to find the...

Question 10

Find the domain of the function. $f ( x ) = \ln \left( x ^ { 2 } + 5 x + 6 \right)$

Accepted Answer

The answer of Find the domain of the function. \(f...

Question 11

Find the exact solution of the equation. $e ^ { 3 x ^ { 4 } } = 10$

Accepted Answer

The answer of Find the exact solution of the equation....

Question 12

Use the Change of Base Formula and a calculator to evaluate the logarithm, correct to six decimal places. Use either natural or common logarithms. $\log _ { 2 } 6$

Accepted Answer

The answer of Use the Change of Base Formula and...

Question 13

A radioactive substance decays in such a way that the amount of mass remaining after t days is given by the function $m ( t ) = 13 e ^ { - 0.015 t }$ where $m ( \text { t })$ Is measured in kilograms. Round your answers to three decimal places. Find the mass at time $t = 0$

Accepted Answer

A)  $13.5 \mathrm {~kg}$ 
B)  $0.015 \mathrm {~kg}$ 
C)  $13.015 \mathrm {~kg}$ 
D)  $15.135 \mathrm {~kg}$ 
E) none of these 
A)  $13.5 \mathrm {~kg}$ 
B)  $0.015 \mathrm {~kg}$ 
C)  $13.015 \mathrm {~kg}$ 
D)  $15.135 \mathrm {~kg}$ 
E) none of these

Question 14

Combine into a single logarithm. $\ln 2 + \ln ( x + 1 ) - [ \ln ( 4 x + 7 ) ] / 3$

Accepted Answer

The answer of Combine into a single logarithm. \(\ln 2...

Question 15

Solve the inequality: $\frac { 1 } { 3 } \leq \log x < 1$

Accepted Answer

A)  $- 30 \leq x < 10$ 
B)  $\sqrt { 10 } + 1 / 3 \leq x < 10$ 
C)  $- 10 \leq x < 10$ 
D)  $\sqrt [ 3 ] { 10 } \leq x < 10 ^ { 3 }$ 
E)  $\sqrt [ 3 ] { 10 } \leq x < 10$ 
A)  $- 30 \leq x < 10$ 
B)  $\sqrt { 10 } + 1 / 3 \leq x < 10$ 
C)  $- 10 \leq x < 10$ 
D)  $\sqrt [ 3 ] { 10 } \leq x < 10 ^ { 3 }$ 
E)  $\sqrt [ 3 ] { 10 } \leq x < 10$

Question 16

Solve the equation. Find the exact solution. $\log x + \log ( x + 1 ) = \log 20$

Accepted Answer

A)  $6$ 
B)  $4$ 
C)  $19$ 
D)  $20$ 
E)  $2$ 
A)  $6$ 
B)  $4$ 
C)  $19$ 
D)  $20$ 
E)  $2$

Question 17

A substance has a hydrogen ion concentration of $\left[ \mathrm { H } ^ {+ } \right] = 4.0 \times 10 ^ { - 3 }$ M. Find the pH of the substance

Accepted Answer

A) pH $\approx 7.4$ 
B) pH $\approx 5.4$ 
C)  pH $\approx 3.4$ 
D) pH $\approx 4.4$ 
E) pH $\approx 2.4$ 
A) pH $\approx 7.4$ 
B) pH $\approx 5.4$ 
C)  pH $\approx 3.4$ 
D) pH $\approx 4.4$ 
E) pH $\approx 2.4$

Question 18

Radium - $221$ has a half-life of $30 \mathrm {~s}$ . Suppose we have a $300 \mathrm {~g}$ sample. 
(a) Find a formula for the mass remaining after$t$ seconds
b) How much of the sample remains after $200$ seconds?
c) After how long will only $20 \mathrm {~g}$ remain?

Accepted Answer

(a) @#LAT-DLM&

b)

Question 19

How long will it take an investment of $\$ 300$ to triple, if the interest rate is $9.5 \%$  per year compounded continuously?

Accepted Answer

The answer of How long will it take an investment...

Question 20

Write the equation in logarithmic form. $25 ^ { - 1 / 2 } = \frac { 1 } { 5 }$

Accepted Answer

A)  $\log _ { 5 } \left( \frac { 1 } { 2 } \right) = 25$ 
B)  $\log _ { 25 } \left( \frac { 1 } { 5 } \right) = - \frac { 1 } { 2 }$ 
C)  $\log _ { 5 } \left( \frac { 1 } { 5 } \right) = - \frac { 1 } { 25 }$ 
D)  $\log _ { 5 } \left( \frac { 1 } { 5 } \right) = - \frac { 1 } { 2 }$ 
E) none of these 
A)  $\log _ { 5 } \left( \frac { 1 } { 2 } \right) = 25$ 
B)  $\log _ { 25 } \left( \frac { 1 } { 5 } \right) = - \frac { 1 } { 2 }$ 
C)  $\log _ { 5 } \left( \frac { 1 } { 5 } \right) = - \frac { 1 } { 25 }$ 
D)  $\log _ { 5 } \left( \frac { 1 } { 5 } \right) = - \frac { 1 } { 2 }$ 
E) none of these

Expand the logarithmic expression. $\ln \left( A B ^ { 2 } C ^ { 3 } \right)$

MaryAnna wants to invest $\$ 6,500$ at an interest rate of $7.5 \%$ Per year, compounded daily. How long will it take her investment to grow to $\$ 8,000 ?$

Combine into a single logarithm. $\ln 2 + \ln ( x + 1 ) - \frac { 1 } { 3 } \ln ( 4 x + 7 )$

Graph the function, not by plotting points, but by starting from the graph of $y = e ^ { x }$ . State the domain, range, and asymptote. $h ( x ) = e ^ { x + 1 } - 5$

Combine into a single logarithm. $\frac { 3 } { 2 } \ln ( x - y ) - 2 \ln \left( x ^ { 2 } + y ^ { 2 } \right)$

Use the Change of Base Formula and a calculator to evaluate the logarithm, correct to six decimal places. Use either natural or common logarithms. $\log _ { 6 } 534$

Find the domain, range, and asymptote of the function. $g ( x ) = 2 + \log _ { 2 } ( x + 4 )$

Sketch the graph of the function. $f ( x ) = 3 + 3 ^ { - x }$

Use a graphing device to find the solutions of the equation, correct to two decimal places. $3 \ln x = 6 - 2 x$

Find the domain of the function. $f ( x ) = \ln \left( x ^ { 2 } + 5 x + 6 \right)$

Find the exact solution of the equation. $e ^ { 3 x ^ { 4 } } = 10$

Use the Change of Base Formula and a calculator to evaluate the logarithm, correct to six decimal places. Use either natural or common logarithms. $\log _ { 2 } 6$

A radioactive substance decays in such a way that the amount of mass remaining after t days is given by the function $m ( t ) = 13 e ^ { - 0.015 t }$ where $m ( \text { t })$ Is measured in kilograms. Round your answers to three decimal places. Find the mass at time $t = 0$

Combine into a single logarithm. $\ln 2 + \ln ( x + 1 ) - [ \ln ( 4 x + 7 ) ] / 3$

Solve the inequality: $\frac { 1 } { 3 } \leq \log x < 1$

Solve the equation. Find the exact solution. $\log x + \log ( x + 1 ) = \log 20$

A substance has a hydrogen ion concentration of $\left[ \mathrm { H } ^ {+ } \right] = 4.0 \times 10 ^ { - 3 }$ M. Find the pH of the substance

Radium - $221$ has a half-life of $30 \mathrm {~s}$ . Suppose we have a $300 \mathrm {~g}$ sample. (a) Find a formula for the mass remaining after $t$ seconds b) How much of the sample remains after $200$ seconds? c) After how long will only $20 \mathrm {~g}$ remain?

How long will it take an investment of $\$ 300$ to triple, if the interest rate is $9.5 \%$ per year compounded continuously?

Write the equation in logarithmic form. $25 ^ { - 1 / 2 } = \frac { 1 } { 5 }$

Equations and Graphs

Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions: Unit Circle Approach

Conic Sections

Polar Coordinates and Parametric Equations

Vectors in Two and Three Dimensions

Systems of Equations and Inequalities

Matrices and Determinants

Conic Sections

Sequences and Series

Counting and Probability

Filters

Exam 5: Trigonometric Functions: Right Triangle Approach

Expand the logarithmic expression. ln⁡(AB2C3)\ln \left( A B ^ { 2 } C ^ { 3 } \right)ln(AB2C3)

MaryAnna wants to invest $6,500\$ 6,500$6,500 at an interest rate of 7.5%7.5 \%7.5% Per year, compounded daily. How long will it take her investment to grow to $8,000?\$ 8,000 ?$8,000?

Combine into a single logarithm. ln⁡2+ln⁡(x+1)−13ln⁡(4x+7)\ln 2 + \ln ( x + 1 ) - \frac { 1 } { 3 } \ln ( 4 x + 7 )ln2+ln(x+1)−31​ln(4x+7)

Graph the function, not by plotting points, but by starting from the graph of y=exy = e ^ { x }y=ex . State the domain, range, and asymptote. h(x)=ex+1−5h ( x ) = e ^ { x + 1 } - 5h(x)=ex+1−5

Combine into a single logarithm. 32ln⁡(x−y)−2ln⁡(x2+y2)\frac { 3 } { 2 } \ln ( x - y ) - 2 \ln \left( x ^ { 2 } + y ^ { 2 } \right)23​ln(x−y)−2ln(x2+y2)

Use the Change of Base Formula and a calculator to evaluate the logarithm, correct to six decimal places. Use either natural or common logarithms. log⁡6534\log _ { 6 } 534log6​534

Find the domain, range, and asymptote of the function. g(x)=2+log⁡2(x+4)g ( x ) = 2 + \log _ { 2 } ( x + 4 )g(x)=2+log2​(x+4)

Sketch the graph of the function. f(x)=3+3−xf ( x ) = 3 + 3 ^ { - x }f(x)=3+3−x

Use a graphing device to find the solutions of the equation, correct to two decimal places. 3ln⁡x=6−2x3 \ln x = 6 - 2 x3lnx=6−2x

Find the domain of the function. f(x)=ln⁡(x2+5x+6)f ( x ) = \ln \left( x ^ { 2 } + 5 x + 6 \right)f(x)=ln(x2+5x+6)

Find the exact solution of the equation. e3x4=10e ^ { 3 x ^ { 4 } } = 10e3x4=10

Use the Change of Base Formula and a calculator to evaluate the logarithm, correct to six decimal places. Use either natural or common logarithms. log⁡26\log _ { 2 } 6log2​6

Combine into a single logarithm. ln⁡2+ln⁡(x+1)−[ln⁡(4x+7)]/3\ln 2 + \ln ( x + 1 ) - [ \ln ( 4 x + 7 ) ] / 3ln2+ln(x+1)−[ln(4x+7)]/3

Solve the inequality: 13≤log⁡x<1\frac { 1 } { 3 } \leq \log x < 131​≤logx<1

Solve the equation. Find the exact solution. log⁡x+log⁡(x+1)=log⁡20\log x + \log ( x + 1 ) = \log 20logx+log(x+1)=log20

A substance has a hydrogen ion concentration of [H+]=4.0×10−3\left[ \mathrm { H } ^ {+ } \right] = 4.0 \times 10 ^ { - 3 }[H+]=4.0×10−3 M. Find the pH of the substance

Radium - 221221221 has a half-life of 30 s30 \mathrm {~s}30 s . Suppose we have a 300 g300 \mathrm {~g}300 g sample. (a) Find a formula for the mass remaining after ttt seconds b) How much of the sample remains after 200200200 seconds? c) After how long will only 20 g20 \mathrm {~g}20 g remain?

How long will it take an investment of $300\$ 300$300 to triple, if the interest rate is 9.5%9.5 \%9.5% per year compounded continuously?

Write the equation in logarithmic form. 25−1/2=1525 ^ { - 1 / 2 } = \frac { 1 } { 5 }25−1/2=51​

Equations and Graphs

Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions: Unit Circle Approach

Conic Sections

Polar Coordinates and Parametric Equations

Vectors in Two and Three Dimensions

Systems of Equations and Inequalities

Matrices and Determinants

Conic Sections

Sequences and Series

Counting and Probability

Filters

Expand the logarithmic expression. $\ln \left( A B ^ { 2 } C ^ { 3 } \right)$

MaryAnna wants to invest $\$ 6,500$ at an interest rate of $7.5 \%$ Per year, compounded daily. How long will it take her investment to grow to $\$ 8,000 ?$

Combine into a single logarithm. $\ln 2 + \ln ( x + 1 ) - \frac { 1 } { 3 } \ln ( 4 x + 7 )$

Graph the function, not by plotting points, but by starting from the graph of $y = e ^ { x }$ . State the domain, range, and asymptote. $h ( x ) = e ^ { x + 1 } - 5$

Combine into a single logarithm. $\frac { 3 } { 2 } \ln ( x - y ) - 2 \ln \left( x ^ { 2 } + y ^ { 2 } \right)$

Use the Change of Base Formula and a calculator to evaluate the logarithm, correct to six decimal places. Use either natural or common logarithms. $\log _ { 6 } 534$

Find the domain, range, and asymptote of the function. $g ( x ) = 2 + \log _ { 2 } ( x + 4 )$

Sketch the graph of the function. $f ( x ) = 3 + 3 ^ { - x }$

Use a graphing device to find the solutions of the equation, correct to two decimal places. $3 \ln x = 6 - 2 x$

Find the domain of the function. $f ( x ) = \ln \left( x ^ { 2 } + 5 x + 6 \right)$

Find the exact solution of the equation. $e ^ { 3 x ^ { 4 } } = 10$

Use the Change of Base Formula and a calculator to evaluate the logarithm, correct to six decimal places. Use either natural or common logarithms. $\log _ { 2 } 6$

Combine into a single logarithm. $\ln 2 + \ln ( x + 1 ) - [ \ln ( 4 x + 7 ) ] / 3$

Solve the inequality: $\frac { 1 } { 3 } \leq \log x < 1$

Solve the equation. Find the exact solution. $\log x + \log ( x + 1 ) = \log 20$

A substance has a hydrogen ion concentration of $\left[ \mathrm { H } ^ {+ } \right] = 4.0 \times 10 ^ { - 3 }$ M. Find the pH of the substance

Radium - $221$ has a half-life of $30 \mathrm {~s}$ . Suppose we have a $300 \mathrm {~g}$ sample. (a) Find a formula for the mass remaining after $t$ seconds b) How much of the sample remains after $200$ seconds? c) After how long will only $20 \mathrm {~g}$ remain?

How long will it take an investment of $\$ 300$ to triple, if the interest rate is $9.5 \%$ per year compounded continuously?

Write the equation in logarithmic form. $25 ^ { - 1 / 2 } = \frac { 1 } { 5 }$