Question 1

Solve the exponential equation algebraically.Approximate the result to three decimal places.   $6 ^ { x } + 8 = 57$

Accepted Answer

A)  $\frac { \ln 49 } { \ln 6 } \approx 2.172$ 
B)  $\frac { \ln 49 } { \ln 6 } \approx - 0.460$ 
C)  $\frac { \ln 49 } { \ln 6 } \approx 0.514$ 
D)  $\frac { \ln 49 } { \ln 6 } \approx 0.460$ 
E)  $\frac { \ln 49 } { \ln 6 } \approx - 2.172$ 
A)  $\frac { \ln 49 } { \ln 6 } \approx 2.172$ 
B)  $\frac { \ln 49 } { \ln 6 } \approx - 0.460$ 
C)  $\frac { \ln 49 } { \ln 6 } \approx 0.514$ 
D)  $\frac { \ln 49 } { \ln 6 } \approx 0.460$ 
E)  $\frac { \ln 49 } { \ln 6 } \approx - 2.172$

Question 2

Identify the graph of the function.  $f ( x ) = \left( \frac { 1 } { 7 } \right) ^ { x }$

Accepted Answer

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

Question 3

Find the exact value of the logarithmic expression without using a calculator. ​
5 ln e7
​

Accepted Answer

A) 7 
B) 35 
C) 5 
D) e 
E) 1 
A) 7 
B) 35 
C) 5 
D) e 
E) 1

Question 4

Simplify the expression.  $\log _ { 5 } 5 ^ { 9 }$

Accepted Answer

A) 45 
B) 5 
C) 9 
D) 81 
E) none of these 
A) 45 
B) 5 
C) 9 
D) 81 
E) none of these

Question 5

Determine whether the statement is true or false given that f(x) = ln x.
​
f(x - 7) = f(x) - f(7), x > 0
​

Accepted Answer

A) True 
 B)False

Question 6

Write the logarithmic equation in exponential form.  $\log _ { 32 } 2 = \frac { 1 } { 5 }$

Accepted Answer

A)  $32 ^ { 1 / 5 } = - 2$ 
B)  $32 ^ { 1 / 5 } = - \frac { 1 } { 2 }$ 
C)  $2 ^ { 1 / 5 } = 32$ 
D)  $32 ^ { 1 / 5 } = 2$ 
E)  $32 ^ { 1 / 5 } = \frac { 1 } { 2 }$ 
A)  $32 ^ { 1 / 5 } = - 2$ 
B)  $32 ^ { 1 / 5 } = - \frac { 1 } { 2 }$ 
C)  $2 ^ { 1 / 5 } = 32$ 
D)  $32 ^ { 1 / 5 } = 2$ 
E)  $32 ^ { 1 / 5 } = \frac { 1 } { 2 }$

Question 7

Find the exponential model $y = a e ^ { 0.5756 x }$ that fits the points shown in the graph.

Accepted Answer

A)  $y = \frac { 1 } { 2 } e ^ { - 0.5756 x }$ 
B)  $y = - \frac { 1 } { 2 } x e ^ { - 0.5756 }$ 
C)  $y = \frac { 1 } { 2 } x e ^ { 0.5756 }$ 
D)  $y = \frac { 1 } { 2 } e ^ { 0.5756 x }$ 
E)  $y = - \frac { 1 } { 2 } e ^ { - 0.5756 x }$ 
A)  $y = \frac { 1 } { 2 } e ^ { - 0.5756 x }$ 
B)  $y = - \frac { 1 } { 2 } x e ^ { - 0.5756 }$ 
C)  $y = \frac { 1 } { 2 } x e ^ { 0.5756 }$ 
D)  $y = \frac { 1 } { 2 } e ^ { 0.5756 x }$ 
E)  $y = - \frac { 1 } { 2 } e ^ { - 0.5756 x }$

Question 8

Match the graph with its exponential function.

Accepted Answer

A)  $y = 4 ^ { x }$ 
B)  $y = - 4 ^ { - x }$ 
C)  $y = - 4 ^ { x }$ 
D)  $y = 4 ^ { - x }$ 
E)  $y = 4 x$ 
A)  $y = 4 ^ { x }$ 
B)  $y = - 4 ^ { - x }$ 
C)  $y = - 4 ^ { x }$ 
D)  $y = 4 ^ { - x }$ 
E)  $y = 4 x$

Question 9

Find the value of x.  $\log _ { 5 } 625 = x$

Accepted Answer

A) x = 625 
B) x = 313 
C) x = 5 
D) x = 4 
A) x = 625 
B) x = 313 
C) x = 5 
D) x = 4

Question 10

Use a calculator to find the value for $\log 0.85759$ to four decimal places.

Accepted Answer

A) -0.0667 
B) -0.1536 
C) 0.9333 
D) -0.9333 
E) 0.0667 
A) -0.0667 
B) -0.1536 
C) 0.9333 
D) -0.9333 
E) 0.0667

Question 11

Find the graph of the function. $y = \log _ { 5 } ( x - 1 )$

Accepted Answer

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

Question 12

Find the magnitude R of an earthquake of intensity $I \left( \text { let } I _ { 0 } = 1 \right. \text { ) }$ .  $I = 16000$

Accepted Answer

A) 3.20 
B) 5.20 
C) 4.20 
D) 2.20 
E) 6.20 
A) 3.20 
B) 5.20 
C) 4.20 
D) 2.20 
E) 6.20

Question 13

Solve the exponential equation algebraically.Approximate the result to three decimal places.   $e ^ { - 4 x ^ { 2 } } = e ^ { 3 x ^ { 2 } - 14 x }$

Accepted Answer

A)  $4,2$ 
B)  $3,2$ 
C)  $- 4,2$ 
D)  $0,2$ 
E)  $0 , - 2$ 
A)  $4,2$ 
B)  $3,2$ 
C)  $- 4,2$ 
D)  $0,2$ 
E)  $0 , - 2$

Question 14

The population P of a culture of bacteria is described by the equation $P = 1600 e ^ { 0.052 t }$ , where t is the time, in hours, relative to the time at which the population was 1600.
(a) What was the population at $t = 3$ hours? Show your work.
(b) After how many hours will the population reach 10000.00? Round to the nearest tenth of an hour.Show your work.

Accepted Answer

@#IMG-DLM& = @#IMG-DLM& = @#IMG-DLM& ≈ @#IMG-DLM& ​
​
(b) @#IMG-DLM& =

Question 15

Evaluate the function at the indicated value of $x = \frac { 1 } { 4 }$ .Round your result to three decimal places. $g ( x ) = - \ln x$

Accepted Answer

A) -1.386 
B) 4 
C) 2.079 
D) -2.079 
E) 1.386 
A) -1.386 
B) 4 
C) 2.079 
D) -2.079 
E) 1.386

Question 16

Solve the exponential equation algebraically.Approximate the result to three decimal places.  $2 \left( 5 ^ { 2 - x } \right) = 12$

Accepted Answer

A)  $2 - \frac { \ln 6 } { \ln 5 } \approx 3.887$ 
B)  $2 - \frac { \ln 6 } { \ln 5 } \approx 1.887$ 
C)  $2 - \frac { \ln 6 } { \ln 5 } \approx 0.887$ 
D)  $2 - \frac { \ln 6 } { \ln 5 } \approx 4.887$ 
E)  $2 - \frac { \ln 6 } { \ln 5 } \approx 2.887$ 
A)  $2 - \frac { \ln 6 } { \ln 5 } \approx 3.887$ 
B)  $2 - \frac { \ln 6 } { \ln 5 } \approx 1.887$ 
C)  $2 - \frac { \ln 6 } { \ln 5 } \approx 0.887$ 
D)  $2 - \frac { \ln 6 } { \ln 5 } \approx 4.887$ 
E)  $2 - \frac { \ln 6 } { \ln 5 } \approx 2.887$

Question 17

Find the exponential model $y = a e ^ { 0.7675 x }$ that fits the points shown in the graph.

Accepted Answer

A)  $y = e ^ { - 0.7675 x }$ 
B)  $y = e ^ { 0.7675 x }$ 
C)  $y = - e ^ { - 0.7675 x }$ 
D)  $y = x e ^ { 0.7675 }$ 
E)  $y = - x e ^ { - 0.7675 }$ 
A)  $y = e ^ { - 0.7675 x }$ 
B)  $y = e ^ { 0.7675 x }$ 
C)  $y = - e ^ { - 0.7675 x }$ 
D)  $y = x e ^ { 0.7675 }$ 
E)  $y = - x e ^ { - 0.7675 }$

Question 18

Evaluate the function at the indicated value of $x = 3$ . 
 $f ( x ) = \log _ { 243 } x$

Accepted Answer

A)  $\frac { 1 } { 5 }$ 
B) -5 
C)  $- \frac { 1 } { 5 }$ 
D) 0 
E) 5 
A)  $\frac { 1 } { 5 }$ 
B) -5 
C)  $- \frac { 1 } { 5 }$ 
D) 0 
E) 5

Question 19

The population P of a culture of bacteria is described by the equation $P = 1300 e ^ { 0.052 t }$ , where t is the time, in hours, relative to the time at which the population was 1300.What was the population at $t = 3$ hours?

Accepted Answer

A)  $P ( 3 ) \approx 1419$ 
B)  $P ( 3 ) \approx 1519$ 
C)  $P ( 3 ) \approx 1319$ 
D)  $P ( 3 ) \approx 1619$ 
E)  $P ( 3 ) \approx 1719$ 
A)  $P ( 3 ) \approx 1419$ 
B)  $P ( 3 ) \approx 1519$ 
C)  $P ( 3 ) \approx 1319$ 
D)  $P ( 3 ) \approx 1619$ 
E)  $P ( 3 ) \approx 1719$

Question 20

Condense the expression to the logarithm of a single quantity.  $\frac { 1 } { 2 } \left[ \log _ { 9 } ( x + 6 ) + 2 \log _ { 9 } ( x - 6 ) \right] - 12 \log _ { 9 } x$

Accepted Answer

A)  $\log _ { 9 } \frac { ( x + 6 ) \sqrt { x - 6 } } { x ^ { 6 } }$ 
B)  $\log _ { 9 } \frac { x ^ { 12 } \sqrt { x - 6 } } { ( x + 6 ) }$ 
C)  $\log _ { 9 } \frac { x ^ { 6 } \sqrt { x - 6 } } { ( x + 6 ) }$ 
D)  $\log _ { 9 } \frac { x ^ { 12 } \sqrt { x + 6 } } { ( x - 6 ) }$ 
E)  $\log _ { 9 } \frac { ( x - 6 ) \sqrt { x + 6 } } { x ^ { 12 } }$ 
A)  $\log _ { 9 } \frac { ( x + 6 ) \sqrt { x - 6 } } { x ^ { 6 } }$ 
B)  $\log _ { 9 } \frac { x ^ { 12 } \sqrt { x - 6 } } { ( x + 6 ) }$ 
C)  $\log _ { 9 } \frac { x ^ { 6 } \sqrt { x - 6 } } { ( x + 6 ) }$ 
D)  $\log _ { 9 } \frac { x ^ { 12 } \sqrt { x + 6 } } { ( x - 6 ) }$ 
E)  $\log _ { 9 } \frac { ( x - 6 ) \sqrt { x + 6 } } { x ^ { 12 } }$

Solve the exponential equation algebraically.Approximate the result to three decimal places. $6 ^ { x } + 8 = 57$

Identify the graph of the function. $f ( x ) = \left( \frac { 1 } { 7 } \right) ^ { x }$

Find the exact value of the logarithmic expression without using a calculator. 5 ln e⁷

Simplify the expression. $\log _ { 5 } 5 ^ { 9 }$

Determine whether the statement is true or false given that f(x) = ln x. f(x - 7) = f(x) - f(7), x > 0

Write the logarithmic equation in exponential form. $\log _ { 32 } 2 = \frac { 1 } { 5 }$

Find the exponential model $y = a e ^ { 0.5756 x }$ that fits the points shown in the graph. $Find the exponential model y = a e ^ { 0.5756 x } that fits the points shown in the graph.$

Match the graph with its exponential function.

Find the value of x. $\log _ { 5 } 625 = x$

Use a calculator to find the value for $\log 0.85759$ to four decimal places.

Find the graph of the function. $y = \log _ { 5 } ( x - 1 )$

Find the magnitude R of an earthquake of intensity $I \left( \text { let } I _ { 0 } = 1 \right. \text { ) }$ . $I = 16000$

Solve the exponential equation algebraically.Approximate the result to three decimal places. $e ^ { - 4 x ^ { 2 } } = e ^ { 3 x ^ { 2 } - 14 x }$

Evaluate the function at the indicated value of $x = \frac { 1 } { 4 }$ .Round your result to three decimal places. $g ( x ) = - \ln x$

Solve the exponential equation algebraically.Approximate the result to three decimal places. $2 \left( 5 ^ { 2 - x } \right) = 12$

Find the exponential model $y = a e ^ { 0.7675 x }$ that fits the points shown in the graph. $Find the exponential model y = a e ^ { 0.7675 x } that fits the points shown in the graph.$

Evaluate the function at the indicated value of $x = 3$ . $f ( x ) = \log _ { 243 } x$

The population P of a culture of bacteria is described by the equation $P = 1300 e ^ { 0.052 t }$ , where t is the time, in hours, relative to the time at which the population was 1300.What was the population at $t = 3$ hours?

Condense the expression to the logarithm of a single quantity. $\frac { 1 } { 2 } \left[ \log _ { 9 } ( x + 6 ) + 2 \log _ { 9 } ( x - 6 ) \right] - 12 \log _ { 9 } x$

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

Exam 3: Exponential and Logarithmic Functions

Solve the exponential equation algebraically.Approximate the result to three decimal places. 6x+8=576 ^ { x } + 8 = 576x+8=57

Identify the graph of the function. f(x)=(17)xf ( x ) = \left( \frac { 1 } { 7 } \right) ^ { x }f(x)=(71​)x

Find the exact value of the logarithmic expression without using a calculator. ​ 5 ln e7 ​

Simplify the expression. log⁡559\log _ { 5 } 5 ^ { 9 }log5​59

Determine whether the statement is true or false given that f(x) = ln x. ​ f(x - 7) = f(x) - f(7), x > 0 ​

Write the logarithmic equation in exponential form. log⁡322=15\log _ { 32 } 2 = \frac { 1 } { 5 }log32​2=51​

Find the exponential model y=ae0.5756xy = a e ^ { 0.5756 x }y=ae0.5756x that fits the points shown in the graph.

Match the graph with its exponential function.

Find the value of x. log⁡5625=x\log _ { 5 } 625 = xlog5​625=x

Use a calculator to find the value for log⁡0.85759\log 0.85759log0.85759 to four decimal places.

Find the graph of the function. y=log⁡5(x−1)y = \log _ { 5 } ( x - 1 )y=log5​(x−1)

Find the magnitude R of an earthquake of intensity I( let I0=1 ) I \left( \text { let } I _ { 0 } = 1 \right. \text { ) }I( let I0​=1 ) . I=16000I = 16000I=16000

Solve the exponential equation algebraically.Approximate the result to three decimal places. e−4x2=e3x2−14xe ^ { - 4 x ^ { 2 } } = e ^ { 3 x ^ { 2 } - 14 x }e−4x2=e3x2−14x

Evaluate the function at the indicated value of x=14x = \frac { 1 } { 4 }x=41​ .Round your result to three decimal places. g(x)=−ln⁡xg ( x ) = - \ln xg(x)=−lnx

Solve the exponential equation algebraically.Approximate the result to three decimal places. 2(52−x)=122 \left( 5 ^ { 2 - x } \right) = 122(52−x)=12

Find the exponential model y=ae0.7675xy = a e ^ { 0.7675 x }y=ae0.7675x that fits the points shown in the graph.

Evaluate the function at the indicated value of x=3x = 3x=3 . f(x)=log⁡243xf ( x ) = \log _ { 243 } xf(x)=log243​x

The population P of a culture of bacteria is described by the equation P=1300e0.052tP = 1300 e ^ { 0.052 t }P=1300e0.052t , where t is the time, in hours, relative to the time at which the population was 1300.What was the population at t=3t = 3t=3 hours?

Condense the expression to the logarithm of a single quantity. 12[log⁡9(x+6)+2log⁡9(x−6)]−12log⁡9x\frac { 1 } { 2 } \left[ \log _ { 9 } ( x + 6 ) + 2 \log _ { 9 } ( x - 6 ) \right] - 12 \log _ { 9 } x21​[log9​(x+6)+2log9​(x−6)]−12log9​x

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

Solve the exponential equation algebraically.Approximate the result to three decimal places. $6 ^ { x } + 8 = 57$

Identify the graph of the function. $f ( x ) = \left( \frac { 1 } { 7 } \right) ^ { x }$

Find the exact value of the logarithmic expression without using a calculator. 5 ln e⁷

Simplify the expression. $\log _ { 5 } 5 ^ { 9 }$

Determine whether the statement is true or false given that f(x) = ln x. f(x - 7) = f(x) - f(7), x > 0

Write the logarithmic equation in exponential form. $\log _ { 32 } 2 = \frac { 1 } { 5 }$

Find the exponential model $y = a e ^ { 0.5756 x }$ that fits the points shown in the graph. $Find the exponential model y = a e ^ { 0.5756 x } that fits the points shown in the graph.$

Find the value of x. $\log _ { 5 } 625 = x$

Use a calculator to find the value for $\log 0.85759$ to four decimal places.

Find the graph of the function. $y = \log _ { 5 } ( x - 1 )$

Find the magnitude R of an earthquake of intensity $I \left( \text { let } I _ { 0 } = 1 \right. \text { ) }$ . $I = 16000$

Solve the exponential equation algebraically.Approximate the result to three decimal places. $e ^ { - 4 x ^ { 2 } } = e ^ { 3 x ^ { 2 } - 14 x }$

Evaluate the function at the indicated value of $x = \frac { 1 } { 4 }$ .Round your result to three decimal places. $g ( x ) = - \ln x$

Solve the exponential equation algebraically.Approximate the result to three decimal places. $2 \left( 5 ^ { 2 - x } \right) = 12$

Find the exponential model $y = a e ^ { 0.7675 x }$ that fits the points shown in the graph. $Find the exponential model y = a e ^ { 0.7675 x } that fits the points shown in the graph.$

Evaluate the function at the indicated value of $x = 3$ . $f ( x ) = \log _ { 243 } x$

The population P of a culture of bacteria is described by the equation $P = 1300 e ^ { 0.052 t }$ , where t is the time, in hours, relative to the time at which the population was 1300.What was the population at $t = 3$ hours?

Condense the expression to the logarithm of a single quantity. $\frac { 1 } { 2 } \left[ \log _ { 9 } ( x + 6 ) + 2 \log _ { 9 } ( x - 6 ) \right] - 12 \log _ { 9 } x$