Question 1

Evaluate the expression without using a calculator. $e ^ { 2 \ln 8 }$

Accepted Answer

A)  $64$ 
B)  $\ln 64$ 
C)  $\ln 8$ 
D)  $16$ 
E)  $\ln 16$ 
A)  $64$ 
B)  $\ln 64$ 
C)  $\ln 8$ 
D)  $16$ 
E)  $\ln 16$

Question 2

Write the equation in logarithmic form. $64 ^ { - 1 / 2 } = \frac { 1 } { 8 }$

Accepted Answer

A)  $\log _ { 64 } \left( \frac { 1 } { 2 } \right) = - 8$ 
B)  $\log _ { 64 } \left( \frac { 1 } { 8 } \right) = - \frac { 1 } { 2 }$ 
C)  $\log _ { 2 } \left( \frac { 1 } { 2 } \right) = - \frac { 1 } { 8 }$ 
D)  $\log _ { 6 } \left( \frac { 1 } { 64 } \right) = \frac { 1 } { 2 }$ 
E)  $\log _ { 64 } ( 2 ) = - 8$ 
A)  $\log _ { 64 } \left( \frac { 1 } { 2 } \right) = - 8$ 
B)  $\log _ { 64 } \left( \frac { 1 } { 8 } \right) = - \frac { 1 } { 2 }$ 
C)  $\log _ { 2 } \left( \frac { 1 } { 2 } \right) = - \frac { 1 } { 8 }$ 
D)  $\log _ { 6 } \left( \frac { 1 } { 64 } \right) = \frac { 1 } { 2 }$ 
E)  $\log _ { 64 } ( 2 ) = - 8$

Question 3

Expand the logarithmic expression. $\ln \left( X Y ^ { 2 } Z ^ { 3 } \right)$

Accepted Answer

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

Question 4

The age of an ancient artifact can be determined by the amount of radioactive carbon-14 remaining in it. If $D _ { 0 }$ is the original amount of carbon-14 and D is the amount remaining, then the artifact's age A (in years) is given by $A = - 8267 \ln \left( \frac { D } { D _ { 0 } } \right)$ Find the age of an object if the amount D of carbon-14 that remains in the object is 85% of the original amount $D _ { 0 }$ 
.

Accepted Answer

The answer of The age of an ancient artifact can...

Question 5

How much more intense is an earthquake with a magnitude of $8.5$ on the Richter scale than one with a magnitude of $5.6$?

Accepted Answer

A)  $1.9$Times 
B)  $79$Times 
C)  $2.9$Times 
D)  $794$Times 
E)  none of these 
A)  $1.9$Times 
B)  $79$Times 
C)  $2.9$Times 
D)  $794$Times 
E)  none of these

Question 6

The velocity of a sky diver t seconds after jumping is given by $v ( t ) = 80 \left( 1 - e ^ { - 02 t } \right)$ . After how many seconds is the velocity 60 ft/s?

Accepted Answer

The answer of The velocity of a sky diver t...

Question 7

Use the Change of Base Formula and a calculator to evaluate the logarithm, correct to six decimal places. Use either natural or common logarithms. $\log _ { 12 } 3.5$

Accepted Answer

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

Question 8

Use a calculator to evaluate the function at the indicated values. Round your answers to three decimals. $g ( x ) = ( 2 / 3 ) ^ { 2 x } ; g ( 0.7 ) , g ( \sqrt { 2 } / 2 ) , g ( 1 / \pi ) , g ( 1 / 3 )$

Accepted Answer

The answer of Use a calculator to evaluate the function...

Question 9

Evaluate the expression without using a calculator. $2 ^ { \log _ { 2 } 13 }$

Accepted Answer

A)  $169$ 
B)  $\ln 13$ 
C)  $\ln 26$ 
D)  $13$ 
E)  $7 / 2$ 
A)  $169$ 
B)  $\ln 13$ 
C)  $\ln 26$ 
D)  $13$ 
E)  $7 / 2$

Question 10

Combine into a single logarithm. $\log ( x - 3 ) + \log ( x + 3 ) - \frac { 1 } { 2 } \log \left( x ^ { 2 } + 9 \right)$

Accepted Answer

The answer of Combine into a single logarithm. \(\log (...

Question 11

Solve the equation. Find the exact solution. $\log x + \log ( x + 1 ) = \log 12$

Accepted Answer

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

Question 12

Graph the function, not by plotting points, but by starting from the graph of $y = e ^ { x }$ 
. State the domain, range, and asymptote. $h ( x ) = e ^ { x - 3 } + 5$

Accepted Answer

Domain: @#LAT-DLM&

Question 13

Evaluate the expression without using a calculator. $\log _ { 6 } 864 - \log _ { 6 } 4$

Accepted Answer

A)  $216$ 
B)  $432$ 
C)  $3$ 
D)  $16$ 
E)  $860$ 
A)  $216$ 
B)  $432$ 
C)  $3$ 
D)  $16$ 
E)  $860$

Question 14

Evaluate the expression without using a calculator. $\log _ { 5 } 500 - \log _ { 5 } 4$

Accepted Answer

A)  $125$ 
B)  $250$ 
C)  $3$ 
D)  $25$ 
E)  $496$ 
A)  $125$ 
B)  $250$ 
C)  $3$ 
D)  $25$ 
E)  $496$

Question 15

Evaluate the expression without using a calculator. $\log _ { 5 } 500 - \log _ { 5 } 4$

Accepted Answer

The answer of Evaluate the expression without using a calculator....

Question 16

Find the solution of the equation $5^{-x/3}=0.63$, correct to four decimal places.

Accepted Answer

The answer of Find the solution of the equation $5^{-x/3}=0.63$,...

Question 17

Expand the logarithmic expression. $\ln \left( x \sqrt { x ^ { 2 } + 1 } \right)$

Accepted Answer

A)  $\ln x + \frac { 1 } { 2 } \ln \left( x ^ { 2 } + 1 \right)$ 
B)  $2 x \ln [ ( x + 1 ) + ( x + 1 ) ]$ 
C)  $2 \ln x - \ln \left( x ^ { 2 } + 1 \right)$ 
D)  $\ln x + \ln \left( x ^ { 2 } - 1 \right)$ 
E)  $\frac { 1 } { 2 } \ln x$ 
A)  $\ln x + \frac { 1 } { 2 } \ln \left( x ^ { 2 } + 1 \right)$ 
B)  $2 x \ln [ ( x + 1 ) + ( x + 1 ) ]$ 
C)  $2 \ln x - \ln \left( x ^ { 2 } + 1 \right)$ 
D)  $\ln x + \ln \left( x ^ { 2 } - 1 \right)$ 
E)  $\frac { 1 } { 2 } \ln x$

Question 18

Write the equation in logarithmic form. $81 ^ { - 1 / 2 } = \frac { 1 } { 9 }$

Accepted Answer

The answer of Write the equation in logarithmic form. \(81...

Question 19

Evaluate the expression without using a calculator. $\log _ { 4 } \left( \frac { 1 } { 64 } \right)$

Accepted Answer

The answer of Evaluate the expression without using a calculator....

Question 20

Find the solution of the equation $3 ^ { x + 2 } = 5 ^ { 2 x }$ 
, correct to four decimal places.

Accepted Answer

The answer of Find the solution of the equation \(3...

Evaluate the expression without using a calculator. $e ^ { 2 \ln 8 }$

Write the equation in logarithmic form. $64 ^ { - 1 / 2 } = \frac { 1 } { 8 }$

Expand the logarithmic expression. $\ln \left( X Y ^ { 2 } Z ^ { 3 } \right)$

How much more intense is an earthquake with a magnitude of $8.5$ on the Richter scale than one with a magnitude of $5.6$ ?

The velocity of a sky diver t seconds after jumping is given by $v ( t ) = 80 \left( 1 - e ^ { - 02 t } \right)$ . After how many seconds is the velocity 60 ft/s?

Use the Change of Base Formula and a calculator to evaluate the logarithm, correct to six decimal places. Use either natural or common logarithms. $\log _ { 12 } 3.5$

Use a calculator to evaluate the function at the indicated values. Round your answers to three decimals. $g ( x ) = ( 2 / 3 ) ^ { 2 x } ; g ( 0.7 ) , g ( \sqrt { 2 } / 2 ) , g ( 1 / \pi ) , g ( 1 / 3 )$

Evaluate the expression without using a calculator. $2 ^ { \log _ { 2 } 13 }$

Combine into a single logarithm. $\log ( x - 3 ) + \log ( x + 3 ) - \frac { 1 } { 2 } \log \left( x ^ { 2 } + 9 \right)$

Solve the equation. Find the exact solution. $\log x + \log ( x + 1 ) = \log 12$

Graph the function, not by plotting points, but by starting from the graph of $y = e ^ { x }$ . State the domain, range, and asymptote. $h ( x ) = e ^ { x - 3 } + 5$

Evaluate the expression without using a calculator. $\log _ { 6 } 864 - \log _ { 6 } 4$

Evaluate the expression without using a calculator. $\log _ { 5 } 500 - \log _ { 5 } 4$

Evaluate the expression without using a calculator. $\log _ { 5 } 500 - \log _ { 5 } 4$

Find the solution of the equation $5^{-x/3}=0.63$ , correct to four decimal places.

Expand the logarithmic expression. $\ln \left( x \sqrt { x ^ { 2 } + 1 } \right)$

Write the equation in logarithmic form. $81 ^ { - 1 / 2 } = \frac { 1 } { 9 }$

Evaluate the expression without using a calculator. $\log _ { 4 } \left( \frac { 1 } { 64 } \right)$

Find the solution of the equation $3 ^ { x + 2 } = 5 ^ { 2 x }$ , correct to four decimal places.

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

Evaluate the expression without using a calculator. e2ln⁡8e ^ { 2 \ln 8 }e2ln8

Write the equation in logarithmic form. 64−1/2=1864 ^ { - 1 / 2 } = \frac { 1 } { 8 }64−1/2=81​

Expand the logarithmic expression. ln⁡(XY2Z3)\ln \left( X Y ^ { 2 } Z ^ { 3 } \right)ln(XY2Z3)

How much more intense is an earthquake with a magnitude of 8.58.58.5 on the Richter scale than one with a magnitude of 5.65.65.6 ?

The velocity of a sky diver t seconds after jumping is given by v(t)=80(1−e−02t)v ( t ) = 80 \left( 1 - e ^ { - 02 t } \right)v(t)=80(1−e−02t) . After how many seconds is the velocity 60 ft/s?

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⁡123.5\log _ { 12 } 3.5log12​3.5

Use a calculator to evaluate the function at the indicated values. Round your answers to three decimals. g(x)=(2/3)2x;g(0.7),g(2/2),g(1/π),g(1/3)g ( x ) = ( 2 / 3 ) ^ { 2 x } ; g ( 0.7 ) , g ( \sqrt { 2 } / 2 ) , g ( 1 / \pi ) , g ( 1 / 3 )g(x)=(2/3)2x;g(0.7),g(2​/2),g(1/π),g(1/3)

Evaluate the expression without using a calculator. 2log⁡2132 ^ { \log _ { 2 } 13 }2log2​13

Combine into a single logarithm. log⁡(x−3)+log⁡(x+3)−12log⁡(x2+9)\log ( x - 3 ) + \log ( x + 3 ) - \frac { 1 } { 2 } \log \left( x ^ { 2 } + 9 \right)log(x−3)+log(x+3)−21​log(x2+9)

Solve the equation. Find the exact solution. log⁡x+log⁡(x+1)=log⁡12\log x + \log ( x + 1 ) = \log 12logx+log(x+1)=log12

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−3+5h ( x ) = e ^ { x - 3 } + 5h(x)=ex−3+5

Evaluate the expression without using a calculator. log⁡6864−log⁡64\log _ { 6 } 864 - \log _ { 6 } 4log6​864−log6​4

Evaluate the expression without using a calculator. log⁡5500−log⁡54\log _ { 5 } 500 - \log _ { 5 } 4log5​500−log5​4

Evaluate the expression without using a calculator. log⁡5500−log⁡54\log _ { 5 } 500 - \log _ { 5 } 4log5​500−log5​4

Find the solution of the equation 5−x/3=0.635^{-x/3}=0.635−x/3=0.63 , correct to four decimal places.

Expand the logarithmic expression. ln⁡(xx2+1)\ln \left( x \sqrt { x ^ { 2 } + 1 } \right)ln(xx2+1​)

Write the equation in logarithmic form. 81−1/2=1981 ^ { - 1 / 2 } = \frac { 1 } { 9 }81−1/2=91​

Evaluate the expression without using a calculator. log⁡4(164)\log _ { 4 } \left( \frac { 1 } { 64 } \right)log4​(641​)

Find the solution of the equation 3x+2=52x3 ^ { x + 2 } = 5 ^ { 2 x }3x+2=52x , correct to four decimal places.

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

Evaluate the expression without using a calculator. $e ^ { 2 \ln 8 }$

Write the equation in logarithmic form. $64 ^ { - 1 / 2 } = \frac { 1 } { 8 }$

Expand the logarithmic expression. $\ln \left( X Y ^ { 2 } Z ^ { 3 } \right)$

How much more intense is an earthquake with a magnitude of $8.5$ on the Richter scale than one with a magnitude of $5.6$ ?

The velocity of a sky diver t seconds after jumping is given by $v ( t ) = 80 \left( 1 - e ^ { - 02 t } \right)$ . After how many seconds is the velocity 60 ft/s?

Use the Change of Base Formula and a calculator to evaluate the logarithm, correct to six decimal places. Use either natural or common logarithms. $\log _ { 12 } 3.5$

Use a calculator to evaluate the function at the indicated values. Round your answers to three decimals. $g ( x ) = ( 2 / 3 ) ^ { 2 x } ; g ( 0.7 ) , g ( \sqrt { 2 } / 2 ) , g ( 1 / \pi ) , g ( 1 / 3 )$

Evaluate the expression without using a calculator. $2 ^ { \log _ { 2 } 13 }$

Combine into a single logarithm. $\log ( x - 3 ) + \log ( x + 3 ) - \frac { 1 } { 2 } \log \left( x ^ { 2 } + 9 \right)$

Solve the equation. Find the exact solution. $\log x + \log ( x + 1 ) = \log 12$

Graph the function, not by plotting points, but by starting from the graph of $y = e ^ { x }$ . State the domain, range, and asymptote. $h ( x ) = e ^ { x - 3 } + 5$

Evaluate the expression without using a calculator. $\log _ { 6 } 864 - \log _ { 6 } 4$

Evaluate the expression without using a calculator. $\log _ { 5 } 500 - \log _ { 5 } 4$

Evaluate the expression without using a calculator. $\log _ { 5 } 500 - \log _ { 5 } 4$

Find the solution of the equation $5^{-x/3}=0.63$ , correct to four decimal places.

Expand the logarithmic expression. $\ln \left( x \sqrt { x ^ { 2 } + 1 } \right)$

Write the equation in logarithmic form. $81 ^ { - 1 / 2 } = \frac { 1 } { 9 }$

Evaluate the expression without using a calculator. $\log _ { 4 } \left( \frac { 1 } { 64 } \right)$

Find the solution of the equation $3 ^ { x + 2 } = 5 ^ { 2 x }$ , correct to four decimal places.