Question 1

Evaluate $g ( x ) = \ln x$ at the indicated value of x.  $x = e ^ { - 9 }$

Accepted Answer

A) 9 
B)  $- \frac { 1 } { 9 }$ 
C) -9 
D)  $\frac { 1 } { 9 }$ 
E)  $e ^ { - 9 }$ 
A) 9 
B)  $- \frac { 1 } { 9 }$ 
C) -9 
D)  $\frac { 1 } { 9 }$ 
E)  $e ^ { - 9 }$

Question 2

Solve the exponential equation algebraically.Approximate the result to three decimal places.   $e ^ { 3 x } = 75$

Accepted Answer

A)  $\frac { \ln 75 } { 3 } \approx 0.439$ 
B)  $\frac { \ln 75 } { 3 } \approx 2.439$ 
C)  $\frac { \ln 75 } { 3 } \approx - 0.561$ 
D)  $\frac { \ln 75 } { 3 } \approx 3.439$ 
E)  $\frac { \ln 75 } { 3 } \approx 1.439$ 
A)  $\frac { \ln 75 } { 3 } \approx 0.439$ 
B)  $\frac { \ln 75 } { 3 } \approx 2.439$ 
C)  $\frac { \ln 75 } { 3 } \approx - 0.561$ 
D)  $\frac { \ln 75 } { 3 } \approx 3.439$ 
E)  $\frac { \ln 75 } { 3 } \approx 1.439$

Question 3

Condense the expression 3(log x - log y) to the logarithm of a single term.

Accepted Answer

A)  $\log \frac { x ^ { 3 } } { y }$ 
B)  $\log \frac { 3 x } { 3 y }$ 
C)  $\log \frac { x } { y ^ { 3 } }$ 
D) 3(log x - log y) 
E)  $\log \left( \frac { x } { y } \right) ^ { 3 }$ 
A)  $\log \frac { x ^ { 3 } } { y }$ 
B)  $\log \frac { 3 x } { 3 y }$ 
C)  $\log \frac { x } { y ^ { 3 } }$ 
D) 3(log x - log y) 
E)  $\log \left( \frac { x } { y } \right) ^ { 3 }$

Question 4

Solve for x.  $\log x = - 4$

Accepted Answer

A)  $- 4$ 
B) 0.0001 
C)  $- 0.0001$ 
D)  $4$ 
E) 1.386 
A)  $- 4$ 
B) 0.0001 
C)  $- 0.0001$ 
D)  $4$ 
E) 1.386

Question 5

Solve the equation algebraically.Round the result to three decimal places.  $\frac { 3 + \ln x } { 8 } = 0$

Accepted Answer

A)  $e ^ { - 3 } \approx 2,980.958$ 
B)  $e ^ { - 3 } \approx 0$ 
C)  $e ^ { - 3 } \approx 54.598$ 
D)  $e ^ { - 3 } \approx 0.050$ 
E)  $e ^ { - 3 } \approx 20.086$ 
A)  $e ^ { - 3 } \approx 2,980.958$ 
B)  $e ^ { - 3 } \approx 0$ 
C)  $e ^ { - 3 } \approx 54.598$ 
D)  $e ^ { - 3 } \approx 0.050$ 
E)  $e ^ { - 3 } \approx 20.086$

Question 6

Evaluate the logarithm using the change-of-base formula.Round your result to three decimal places.
​
Log2 7
​

Accepted Answer

A) 2.807 
B) 6.807 
C) 4.807 
D) 5.807 
E) 3.807 
A) 2.807 
B) 6.807 
C) 4.807 
D) 5.807 
E) 3.807

Question 7

Use a graphing utility to graph the functions given by 
Y1 = ln x - ln (x - 4)

And
 $y _ { 2 } = \ln \frac { x } { x - 4 }$ 
In the same viewing window.

Accepted Answer

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

Question 8

The population P of a bacteria culture is modeled by $P = 4100 e ^ { k t }$ , where t is the time in hours.If the population of the culture was 5800 after 40 hours, how long does it take for the population to double? Round to the nearest tenth of an hour.

Accepted Answer

A) 54.8 hours 
B) 8.9 hours 
C) 79.9 hours 
D) 81.7 hours 
E) 56.6 hours 
A) 54.8 hours 
B) 8.9 hours 
C) 79.9 hours 
D) 81.7 hours 
E) 56.6 hours

Question 9

Determine whether the statement is true or false given that f(x) = ln x.
​
f(8x) = f(8) + f(x), x > 0
​

Accepted Answer

A) True 
 B)False

Question 10

Solve the exponential equation algebraically.Approximate the result to three decimal places.  $e ^ { x } = e ^ { x ^ { 2 } - 30 }$

Accepted Answer

A)  $- 6 , - 5$ 
B)  $1 , - 30$ 
C)  $6,5$ 
D)  $- 6,5$ 
E)  $6 , - 5$ 
A)  $- 6 , - 5$ 
B)  $1 , - 30$ 
C)  $6,5$ 
D)  $- 6,5$ 
E)  $6 , - 5$

Question 11

Write the exponential equation in logarithmic form. ? $24 ^ { 2 } = 576$

Accepted Answer

A)  $\log _ { 24 } 576 = 2$ 
B)  $\log _ { 24 } 576 = \frac { 1 } { 2 }$ 
C)  $\log _ { 576 } 24 = 2$ 
D)  $\log _ { 24 } 576 = - 2$ 
E)  $\log _ { 24 } 2 = 576$ 
A)  $\log _ { 24 } 576 = 2$ 
B)  $\log _ { 24 } 576 = \frac { 1 } { 2 }$ 
C)  $\log _ { 576 } 24 = 2$ 
D)  $\log _ { 24 } 576 = - 2$ 
E)  $\log _ { 24 } 2 = 576$

Question 12

Solve the exponential equation algebraically.Approximate the result to three decimal places.   $e ^ { x } - 6 = 13$

Accepted Answer

A)  $\ln 19 \approx - 2.565$ 
B)  $\ln 19 \approx 2.944$ 
C)  $\ln 19 \approx 1.792$ 
D)  $\ln 19 \approx 2.565$ 
E)  $\ln 19 \approx - 2.944$ 
A)  $\ln 19 \approx - 2.565$ 
B)  $\ln 19 \approx 2.944$ 
C)  $\ln 19 \approx 1.792$ 
D)  $\ln 19 \approx 2.565$ 
E)  $\ln 19 \approx - 2.944$

Question 13

If $1 is invested in an account over a 10-year period, the amount in the account, where t represents the time in years, is given by $A = 1 + 0.075 \| t \mid \| \text { or } A = e ^ { 0.07 t }$ depending on whether the account pays simple interest at $7 \frac { 1 } { 2 } \%$ or continuous compound interest at 7%.Graph each function on the same set of axes.Which grows at a higher rate?

Accepted Answer

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

Question 14

Find the exact value of the logarithmic expression without using a calculator.  $\log _ { 7 } \sqrt [ 3 ] { 7 }$

Accepted Answer

A) 3 
B)  $\frac { 1 } { 3 }$ 
C) 7 
D) 21 
E) None of these 
A) 3 
B)  $\frac { 1 } { 3 }$ 
C) 7 
D) 21 
E) None of these

Question 15

Evaluate the function at the indicated value of $x = 1$ . $f ( x ) = \log _ { 8 } x$

Accepted Answer

A)  $\frac { 1 } { 8 }$ 
B)  $- \frac { 1 } { 8 }$ 
C) -8 
D) 0 
E) 8 
A)  $\frac { 1 } { 8 }$ 
B)  $- \frac { 1 } { 8 }$ 
C) -8 
D) 0 
E) 8

Question 16

Write the logarithmic equation in exponential form.  $\log _ { 7 } \frac { 1 } { 49 } = - 2$

Accepted Answer

A)  $7 ^ { - 2 } = - \frac { 1 } { 49 }$ 
B)  $7 ^ { - 2 } = \frac { 1 } { 49 }$ 
C)  $7 ^ { - 2 } = - 49$ 
D)  $7 ^ { - 2 } = 49$ 
E)  $49 ^ { - 2 } = \frac { 1 } { 7 }$ 
A)  $7 ^ { - 2 } = - \frac { 1 } { 49 }$ 
B)  $7 ^ { - 2 } = \frac { 1 } { 49 }$ 
C)  $7 ^ { - 2 } = - 49$ 
D)  $7 ^ { - 2 } = 49$ 
E)  $49 ^ { - 2 } = \frac { 1 } { 7 }$

Question 17

Assume that x, y, z and b are positive numbers.Use the properties of logarithms to write the expression $\log _ { b } \sqrt [ 4 ] { \frac { x ^ { 5 } y ^ { 2 } } { z ^ { 4 } } }$ in terms of the logarithms of x, y, and z.

Accepted Answer

A)  $\frac { 5 } { 4 } \log _ { b } x + \log _ { b } y - \log _ { b } z$ 
B)  $\frac { 5 } { 4 } \log _ { b } x + \frac { 1 } { 2 } \log _ { b } y - \log _ { b } z$ 
C)  $\log _ { b } x + \frac { 1 } { 2 } \log _ { b } y - \log _ { b } z$ 
D)  $\frac { 5 } { 4 } \log _ { b } ( x + y + z )$ 
E)  $20 \log _ { b } x + 8 \log _ { b } y - 16 \log _ { b } z$ 
A)  $\frac { 5 } { 4 } \log _ { b } x + \log _ { b } y - \log _ { b } z$ 
B)  $\frac { 5 } { 4 } \log _ { b } x + \frac { 1 } { 2 } \log _ { b } y - \log _ { b } z$ 
C)  $\log _ { b } x + \frac { 1 } { 2 } \log _ { b } y - \log _ { b } z$ 
D)  $\frac { 5 } { 4 } \log _ { b } ( x + y + z )$ 
E)  $20 \log _ { b } x + 8 \log _ { b } y - 16 \log _ { b } z$

Question 18

The chemical acidity of a solution is measured in units of pH: $\mathrm { pH } = - \log \left[ \mathrm { H } ^ { + } \right]$ , where $\left[ \mathrm { H } ^ { + } \right]$ is the hydrogen ion concentration in the solution.If a sample of rain has a pH of 3.4, how many times higher is its $\left[ \mathrm { H } ^ { + } \right]$ than pure water's, which has a pH of 7?

Accepted Answer

A)  $4.0 \times 10 ^ { 3 }$ 
B)  $2.5 \times 10 ^ { 4 }$ 
C) 7 
D)  $2.5 \times 10 ^ { 3 }$ 
E)  $4.0 \times 10 ^ { 4 }$ 
A)  $4.0 \times 10 ^ { 3 }$ 
B)  $2.5 \times 10 ^ { 4 }$ 
C) 7 
D)  $2.5 \times 10 ^ { 3 }$ 
E)  $4.0 \times 10 ^ { 4 }$

Question 19

Rewrite the logarithm log6 412 in terms of the common logarithm (base 10).

Accepted Answer

A) log 6 log 412 
B)  $\frac { \log 412 } { \log 6 }$ 
C)  $\frac { \log 6 } { \log 412 }$ 
D) log 412 
E)  $\frac { \log 412 } { \log _ { 6 } 10 }$ 
A) log 6 log 412 
B)  $\frac { \log 412 } { \log 6 }$ 
C)  $\frac { \log 6 } { \log 412 }$ 
D) log 412 
E)  $\frac { \log 412 } { \log _ { 6 } 10 }$

Question 20

Find the intensity I of an earthquake measuring R on the Richter scale $\left( \text { let } I _ { 0 } = 1 \right)$ . 
Southern Sumatra, Indonesia in 2007, $R = 8.25$

Accepted Answer

A)  $10 ^ { 8.25 } \approx 177,822,941$ 
B)  $10 ^ { 8.25 } \approx 177,827,941$ 
C)  $10 ^ { 8.25 } \approx 177,825,941$ 
D)  $10 ^ { 8.25 } \approx 177,832,941$ 
E)  $10 ^ { 8.25 } \approx 177,829,941$ 
A)  $10 ^ { 8.25 } \approx 177,822,941$ 
B)  $10 ^ { 8.25 } \approx 177,827,941$ 
C)  $10 ^ { 8.25 } \approx 177,825,941$ 
D)  $10 ^ { 8.25 } \approx 177,832,941$ 
E)  $10 ^ { 8.25 } \approx 177,829,941$

Evaluate $g ( x ) = \ln x$ at the indicated value of x. $x = e ^ { - 9 }$

Solve the exponential equation algebraically.Approximate the result to three decimal places. $e ^ { 3 x } = 75$

Condense the expression 3(log x - log y) to the logarithm of a single term.

Solve for x. $\log x = - 4$

Solve the equation algebraically.Round the result to three decimal places. $\frac { 3 + \ln x } { 8 } = 0$

Evaluate the logarithm using the change-of-base formula.Round your result to three decimal places. Log₂ 7

Use a graphing utility to graph the functions given by Y₁ = ln x - ln (x - 4) And $y _ { 2 } = \ln \frac { x } { x - 4 }$ In the same viewing window.

The population P of a bacteria culture is modeled by $P = 4100 e ^ { k t }$ , where t is the time in hours.If the population of the culture was 5800 after 40 hours, how long does it take for the population to double? Round to the nearest tenth of an hour.

Determine whether the statement is true or false given that f(x) = ln x. f(8x) = f(8) + f(x), x > 0

Solve the exponential equation algebraically.Approximate the result to three decimal places. $e ^ { x } = e ^ { x ^ { 2 } - 30 }$

Write the exponential equation in logarithmic form. ? $24 ^ { 2 } = 576$

Solve the exponential equation algebraically.Approximate the result to three decimal places. $e ^ { x } - 6 = 13$

Find the exact value of the logarithmic expression without using a calculator. $\log _ { 7 } \sqrt [ 3 ] { 7 }$

Evaluate the function at the indicated value of $x = 1$ . $f ( x ) = \log _ { 8 } x$

Write the logarithmic equation in exponential form. $\log _ { 7 } \frac { 1 } { 49 } = - 2$

Assume that x, y, z and b are positive numbers.Use the properties of logarithms to write the expression $\log _ { b } \sqrt [ 4 ] { \frac { x ^ { 5 } y ^ { 2 } } { z ^ { 4 } } }$ in terms of the logarithms of x, y, and z.

Rewrite the logarithm log₆ 412 in terms of the common logarithm (base 10).

Find the intensity I of an earthquake measuring R on the Richter scale $\left( \text { let } I _ { 0 } = 1 \right)$ . Southern Sumatra, Indonesia in 2007, $R = 8.25$

Functions and Their Graphs

Polynomial and Rational Functions

Trigonometry

Analytic Trigonometry

Additional Topics In Trigonometery

Systems Of Equations and Inequalities

Matrices and Determinants

Sequences Series and Probability

Topics In Analytic Geometry

Analytic Geometry In Three Dimensions

Limits and An Introduction To Calculus

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Exam 3: Exponential and Logarithmic Functions

Evaluate g(x)=ln⁡xg ( x ) = \ln xg(x)=lnx at the indicated value of x. x=e−9x = e ^ { - 9 }x=e−9

Solve the exponential equation algebraically.Approximate the result to three decimal places. e3x=75e ^ { 3 x } = 75e3x=75

Condense the expression 3(log x - log y) to the logarithm of a single term.

Solve for x. log⁡x=−4\log x = - 4logx=−4

Solve the equation algebraically.Round the result to three decimal places. 3+ln⁡x8=0\frac { 3 + \ln x } { 8 } = 083+lnx​=0

Evaluate the logarithm using the change-of-base formula.Round your result to three decimal places. ​ Log2 7 ​

Use a graphing utility to graph the functions given by Y1 = ln x - ln (x - 4) And y2=ln⁡xx−4y _ { 2 } = \ln \frac { x } { x - 4 }y2​=lnx−4x​ In the same viewing window.

The population P of a bacteria culture is modeled by P=4100ektP = 4100 e ^ { k t }P=4100ekt , where t is the time in hours.If the population of the culture was 5800 after 40 hours, how long does it take for the population to double? Round to the nearest tenth of an hour.

Determine whether the statement is true or false given that f(x) = ln x. ​ f(8x) = f(8) + f(x), x > 0 ​

Solve the exponential equation algebraically.Approximate the result to three decimal places. ex=ex2−30e ^ { x } = e ^ { x ^ { 2 } - 30 }ex=ex2−30

Write the exponential equation in logarithmic form. ? 242=57624 ^ { 2 } = 576242=576

Solve the exponential equation algebraically.Approximate the result to three decimal places. ex−6=13e ^ { x } - 6 = 13ex−6=13

Find the exact value of the logarithmic expression without using a calculator. log⁡773\log _ { 7 } \sqrt [ 3 ] { 7 }log7​37​

Evaluate the function at the indicated value of x=1x = 1x=1 . f(x)=log⁡8xf ( x ) = \log _ { 8 } xf(x)=log8​x

Write the logarithmic equation in exponential form. log⁡7149=−2\log _ { 7 } \frac { 1 } { 49 } = - 2log7​491​=−2

Assume that x, y, z and b are positive numbers.Use the properties of logarithms to write the expression log⁡bx5y2z44\log _ { b } \sqrt [ 4 ] { \frac { x ^ { 5 } y ^ { 2 } } { z ^ { 4 } } }logb​4z4x5y2​​ in terms of the logarithms of x, y, and z.

Rewrite the logarithm log6 412 in terms of the common logarithm (base 10).

Find the intensity I of an earthquake measuring R on the Richter scale ( let I0=1)\left( \text { let } I _ { 0 } = 1 \right)( let I0​=1) . Southern Sumatra, Indonesia in 2007, R=8.25R = 8.25R=8.25

Functions and Their Graphs

Polynomial and Rational Functions

Trigonometry

Analytic Trigonometry

Additional Topics In Trigonometery

Systems Of Equations and Inequalities

Matrices and Determinants

Sequences Series and Probability

Topics In Analytic Geometry

Analytic Geometry In Three Dimensions

Limits and An Introduction To Calculus

Filters

Evaluate $g ( x ) = \ln x$ at the indicated value of x. $x = e ^ { - 9 }$

Solve the exponential equation algebraically.Approximate the result to three decimal places. $e ^ { 3 x } = 75$

Solve for x. $\log x = - 4$

Solve the equation algebraically.Round the result to three decimal places. $\frac { 3 + \ln x } { 8 } = 0$

Evaluate the logarithm using the change-of-base formula.Round your result to three decimal places. Log₂ 7

Use a graphing utility to graph the functions given by Y₁ = ln x - ln (x - 4) And $y _ { 2 } = \ln \frac { x } { x - 4 }$ In the same viewing window.

The population P of a bacteria culture is modeled by $P = 4100 e ^ { k t }$ , where t is the time in hours.If the population of the culture was 5800 after 40 hours, how long does it take for the population to double? Round to the nearest tenth of an hour.

Determine whether the statement is true or false given that f(x) = ln x. f(8x) = f(8) + f(x), x > 0

Solve the exponential equation algebraically.Approximate the result to three decimal places. $e ^ { x } = e ^ { x ^ { 2 } - 30 }$

Write the exponential equation in logarithmic form. ? $24 ^ { 2 } = 576$

Solve the exponential equation algebraically.Approximate the result to three decimal places. $e ^ { x } - 6 = 13$

Find the exact value of the logarithmic expression without using a calculator. $\log _ { 7 } \sqrt [ 3 ] { 7 }$

Evaluate the function at the indicated value of $x = 1$ . $f ( x ) = \log _ { 8 } x$

Write the logarithmic equation in exponential form. $\log _ { 7 } \frac { 1 } { 49 } = - 2$

Assume that x, y, z and b are positive numbers.Use the properties of logarithms to write the expression $\log _ { b } \sqrt [ 4 ] { \frac { x ^ { 5 } y ^ { 2 } } { z ^ { 4 } } }$ in terms of the logarithms of x, y, and z.

Rewrite the logarithm log₆ 412 in terms of the common logarithm (base 10).

Find the intensity I of an earthquake measuring R on the Richter scale $\left( \text { let } I _ { 0 } = 1 \right)$ . Southern Sumatra, Indonesia in 2007, $R = 8.25$