Question 1

Find the decibel intensity level at a crowded football game if the intensity was measured at $3.98 \times 10 ^ { - 3 }$ $\text{ watts/m}^2$

Accepted Answer

A)  $12 \mathrm {~dB}$ 
B)  $114 \mathrm {~dB}$ 
C)  $52 \mathrm {~dB}$ 
D)  $88 \mathrm {~dB}$ 
E)  none of these 
A)  $12 \mathrm {~dB}$ 
B)  $114 \mathrm {~dB}$ 
C)  $52 \mathrm {~dB}$ 
D)  $88 \mathrm {~dB}$ 
E)  none of these

Question 2

Find the decibel intensity level at a rock concert if the intensity was measured at $3.98 \times 10 ^ { - 3 }$  $\text {watts/m }^2 $

Accepted Answer

A)  $12 \mathrm {~dB}$ 
B)  $114 \mathrm {~dB}$ 
C)  $52 \mathrm {~dB}$ 
D)  $88 \mathrm {~dB}$ 
E)  none of these 
A)  $12 \mathrm {~dB}$ 
B)  $114 \mathrm {~dB}$ 
C)  $52 \mathrm {~dB}$ 
D)  $88 \mathrm {~dB}$ 
E)  none of these

Question 3

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

Accepted Answer

The answer of Write the equation in logarithmic form. \(64...

Question 4

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

Accepted Answer

A)  Domain: $( - 4 , \infty )$
, Range: $( - 4 , \infty )$
, 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: $( - 4 , \infty )$
, 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 5

The intensity level of sound at a crowded football game was measured at $96$ 
dB. Find the intensity in $\text {watts/m }^2 $

Accepted Answer

The answer of The intensity level of sound at a...

Question 6

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

The answer of A substance has a hydrogen ion concentration...

Question 7

A certain strain of bacteria divides every three hours. If a colony is started with 50 bacteria, then the time t (in hours) required for the colony to grow to N bacteria is given by $t = 3 \frac { \log ( N / 50 ) } { \log 2 }$ Find the time required for the colony to grow to five million bacteria

Accepted Answer

A)  458.61 hr 
B)  49.83 hr 
C)  45.86 hr 
D)  35.86 hr 
E)  none of these 
A)  458.61 hr 
B)  49.83 hr 
C)  45.86 hr 
D)  35.86 hr 
E)  none of these

Question 8

Expand the logarithmic expression. $\log _ { 6 } \left( \frac { 4 x ^ { 3 } } { \sqrt { y } ( x - 2 ) ^ { 6 } } \right)$

Accepted Answer

A)  $3 \log _ { 6 } 2 + 2 \log _ { 6 } x - \frac { 1 } { 2 } \log _ { 6 } y - 6 \log _ { 6 } ( x - 2 )$ 
B)  $\log _ { 6 } 2 + 3 \log _ { 6 } x - 2 \log _ { 6 } y - 6 \log _ { 6 } ( x - 2 )$ 
C)  $2 \log _ { 6 } 2 + 3 \log _ { 6 } x - \frac { 1 } { 2 } \log _ { 6 } y + 6 \log _ { 6 } ( x - 2 )$ 
D)  $2 \log _ { 6 } 2 - 3 \log _ { 6 } x - \log _ { 6 } y - \frac { 1 } { 2 } \log _ { 6 } ( x - 6 )$ 
E)  none 
A)  $3 \log _ { 6 } 2 + 2 \log _ { 6 } x - \frac { 1 } { 2 } \log _ { 6 } y - 6 \log _ { 6 } ( x - 2 )$ 
B)  $\log _ { 6 } 2 + 3 \log _ { 6 } x - 2 \log _ { 6 } y - 6 \log _ { 6 } ( x - 2 )$ 
C)  $2 \log _ { 6 } 2 + 3 \log _ { 6 } x - \frac { 1 } { 2 } \log _ { 6 } y + 6 \log _ { 6 } ( x - 2 )$ 
D)  $2 \log _ { 6 } 2 - 3 \log _ { 6 } x - \log _ { 6 } y - \frac { 1 } { 2 } \log _ { 6 } ( x - 6 )$ 
E)  none

Question 9

A substance has a hydrogen ion concentration of $\left[ \mathrm { H } ^ { + } \right] = 3.7 \times 10 ^ { - 6 }$ M. Find the pH of the substance.

Accepted Answer

The answer of A substance has a hydrogen ion concentration...

Question 10

Solve the equation. Find the exact solution. $ e^{3 x / 5}=7 $

Accepted Answer

A)  $x = - \frac { 5 } { 3 } \ln 7$ 
B)  $x = \frac { 7 } { 3 }$ 
C)  $x = \frac { 7 } { 3 } \ln 5$ 
D)  $x = 7 \ln ( 5 / 3 )$ 
E)  $x = \frac { e } { 7 } \ln 3$ 
A)  $x = - \frac { 5 } { 3 } \ln 7$ 
B)  $x = \frac { 7 } { 3 }$ 
C)  $x = \frac { 7 } { 3 } \ln 5$ 
D)  $x = 7 \ln ( 5 / 3 )$ 
E)  $x = \frac { e } { 7 } \ln 3$

Question 11

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

A)  $0.544068$ 
B)  $3.737670$ 
C)  $0.504149$ 
D)  $1.252763$ 
E)  $2.484907$ 
A)  $0.544068$ 
B)  $3.737670$ 
C)  $0.504149$ 
D)  $1.252763$ 
E)  $2.484907$

Question 12

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

Accepted Answer

The answer of Combine into a single logarithm. \(\frac {...

Question 13

Write the equation in exponential form. $\ln k=19$

Accepted Answer

The answer of Write the equation in exponential form. \(\ln...

Question 14

Solve the equation. Find the exact solution. $\log _ { 3 } ( x + 5 ) - \log _ { 3 } ( x - 2 ) = 1$

Accepted Answer

A)  $5$ 
B)  $4$ 
C)  $3$ 
D)  $7$ 
E)  $1$ 
A)  $5$ 
B)  $4$ 
C)  $3$ 
D)  $7$ 
E)  $1$

Question 15

Solve the inequality: $0.5 \leq \log x < 1$

Accepted Answer

A)  $10 \leq x < 1$ 
B)  $\sqrt { 10 } + 1 / 2 \leq x < 10$ 
C)  $- 10 \leq x < 10$ 
D)  $\sqrt { 10 } \leq x < 10 ^ { 2 }$ 
E)  $\sqrt { 10 } \leq x < 10$ 
A)  $10 \leq x < 1$ 
B)  $\sqrt { 10 } + 1 / 2 \leq x < 10$ 
C)  $- 10 \leq x < 10$ 
D)  $\sqrt { 10 } \leq x < 10 ^ { 2 }$ 
E)  $\sqrt { 10 } \leq x < 10$

Question 16

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

Accepted Answer

A)  $\frac { \ln X + 2 \ln Y } { 3 \ln Z }$ 
B)  $\frac { 2 \ln X + \ln Y ^ { 2 } } { 3 Z }$ 
C)  $\ln ( \mathrm { X } + 2 \mathrm { Y } + 3 \mathrm { Z } )$ 
D)  $\ln X + 2 \ln Y + 3 \ln Z$ 
E)  $6 \ln ( X + Y + Z )$ 
A)  $\frac { \ln X + 2 \ln Y } { 3 \ln Z }$ 
B)  $\frac { 2 \ln X + \ln Y ^ { 2 } } { 3 Z }$ 
C)  $\ln ( \mathrm { X } + 2 \mathrm { Y } + 3 \mathrm { Z } )$ 
D)  $\ln X + 2 \ln Y + 3 \ln Z$ 
E)  $6 \ln ( X + Y + Z )$

Find the decibel intensity level at a crowded football game if the intensity was measured at $3.98 \times 10 ^ { - 3 }$ $\text{ watts/m}^2$

Find the decibel intensity level at a rock concert if the intensity was measured at $3.98 \times 10 ^ { - 3 }$ $\text {watts/m }^2$

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

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

The intensity level of sound at a crowded football game was measured at $96$ dB. Find the intensity in $\text {watts/m }^2$

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

A certain strain of bacteria divides every three hours. If a colony is started with 50 bacteria, then the time t (in hours) required for the colony to grow to N bacteria is given by $t = 3 \frac { \log ( N / 50 ) } { \log 2 }$ Find the time required for the colony to grow to five million bacteria

Expand the logarithmic expression. $\log _ { 6 } \left( \frac { 4 x ^ { 3 } } { \sqrt { y } ( x - 2 ) ^ { 6 } } \right)$

A substance has a hydrogen ion concentration of $\left[ \mathrm { H } ^ { + } \right] = 3.7 \times 10 ^ { - 6 }$ M. Find the pH of the substance.

Solve the equation. Find the exact solution. $e^{3 x / 5}=7$

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

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

Write the equation in exponential form. $\ln k=19$

Solve the equation. Find the exact solution. $\log _ { 3 } ( x + 5 ) - \log _ { 3 } ( x - 2 ) = 1$

Solve the inequality: $0.5 \leq \log x < 1$

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

Equations and Graphs

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Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions: Unit Circle Approach

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Exam 5: Trigonometric Functions: Right Triangle Approach

Find the decibel intensity level at a crowded football game if the intensity was measured at 3.98×10−33.98 \times 10 ^ { - 3 }3.98×10−3 watts/m2\text{ watts/m}^2 watts/m2

Find the decibel intensity level at a rock concert if the intensity was measured at 3.98×10−33.98 \times 10 ^ { - 3 }3.98×10−3 watts/m 2\text {watts/m }^2 watts/m 2

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

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

The intensity level of sound at a crowded football game was measured at 969696 dB. Find the intensity in watts/m 2\text {watts/m }^2 watts/m 2

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.

Expand the logarithmic expression. log⁡6(4x3y(x−2)6)\log _ { 6 } \left( \frac { 4 x ^ { 3 } } { \sqrt { y } ( x - 2 ) ^ { 6 } } \right)log6​(y​(x−2)64x3​)

A substance has a hydrogen ion concentration of [H+]=3.7×10−6\left[ \mathrm { H } ^ { + } \right] = 3.7 \times 10 ^ { - 6 }[H+]=3.7×10−6 M. Find the pH of the substance.

Solve the equation. Find the exact solution. e3x/5=7 e^{3 x / 5}=7 e3x/5=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⁡123.5\log _ { 12 } 3.5log12​3.5

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)

Write the equation in exponential form. ln⁡k=19\ln k=19lnk=19

Solve the equation. Find the exact solution. log⁡3(x+5)−log⁡3(x−2)=1\log _ { 3 } ( x + 5 ) - \log _ { 3 } ( x - 2 ) = 1log3​(x+5)−log3​(x−2)=1

Solve the inequality: 0.5≤log⁡x<10.5 \leq \log x < 10.5≤logx<1

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

Equations and Graphs

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Polynomial and Rational Functions

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Find the decibel intensity level at a crowded football game if the intensity was measured at $3.98 \times 10 ^ { - 3 }$ $\text{ watts/m}^2$

Find the decibel intensity level at a rock concert if the intensity was measured at $3.98 \times 10 ^ { - 3 }$ $\text {watts/m }^2$

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

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

The intensity level of sound at a crowded football game was measured at $96$ dB. Find the intensity in $\text {watts/m }^2$

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

Expand the logarithmic expression. $\log _ { 6 } \left( \frac { 4 x ^ { 3 } } { \sqrt { y } ( x - 2 ) ^ { 6 } } \right)$

A substance has a hydrogen ion concentration of $\left[ \mathrm { H } ^ { + } \right] = 3.7 \times 10 ^ { - 6 }$ M. Find the pH of the substance.

Solve the equation. Find the exact solution. $e^{3 x / 5}=7$

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

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

Write the equation in exponential form. $\ln k=19$

Solve the equation. Find the exact solution. $\log _ { 3 } ( x + 5 ) - \log _ { 3 } ( x - 2 ) = 1$

Solve the inequality: $0.5 \leq \log x < 1$

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