Question 1

Identify the graph that represents the function.
$$y = 5 e ^ { - 2 ( x - 1 ) ^ { 2 } }$$

Accepted Answer

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

Question 2

Solve the logarithmic equation below algebraically. Round your result to three decimal places. $5 \log _ { 4 } ( x + 1 ) = 12$

Accepted Answer

A)  21.326 
B)  22.244 
C)  23.558 
D)  23.291 
E)  26.858 
A)  21.326 
B)  22.244 
C)  23.558 
D)  23.291 
E)  26.858

Question 3

Condense the expression $\frac { 1 } { 5 } \left[ \log _ { 4 } x + \log _ { 4 } 6 \right] - \left[ \log _ { 4 } y \right]$ to the logarithm of a single term.

Accepted Answer

A)  $\log _ { 4 } \frac { ( 6 x ) ^ { 5 } } { y }$ 
B)  $\log _ { 4 } \frac { 6 x } { 5 y }$ 
C)  $\log _ { 4 } \sqrt [ 5 ] { \frac { 6 x } { y } }$ 
D)  $\log _ { 4 } \frac { \sqrt [ 5 ] { 6 x } } { y }$ 
E)  $\log _ { 4 } \sqrt [ 5 ] { 6 x } - \log _ { 4 } y$ 
A)  $\log _ { 4 } \frac { ( 6 x ) ^ { 5 } } { y }$ 
B)  $\log _ { 4 } \frac { 6 x } { 5 y }$ 
C)  $\log _ { 4 } \sqrt [ 5 ] { \frac { 6 x } { y } }$ 
D)  $\log _ { 4 } \frac { \sqrt [ 5 ] { 6 x } } { y }$ 
E)  $\log _ { 4 } \sqrt [ 5 ] { 6 x } - \log _ { 4 } y$

Question 4

Identify the graph that represents the function.
$y = \ln \frac { 1 } { x + 1 }$

Accepted Answer

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

Question 5

What is the value of the function $f ( x ) = 3.8 e ^ { - 1.5 x }$ at $x = 2.5 ?$ Round to 3 decimal places.

Accepted Answer

A)  $0.848$ 
B)  $0.089$ 
C)  $10.329$ 
D)  $- 38.736$ 
E)  $0.001$ 
A)  $0.848$ 
B)  $0.089$ 
C)  $10.329$ 
D)  $- 38.736$ 
E)  $0.001$

Question 6

Evaluate the function $f ( x ) = \log _ { 4 } x$ at $x = \frac { 1 } { 16 }$ without using a calculator.

Accepted Answer

A)  $- 1$ 
B)  $- 2$ 
C)  $- 3$ 
D)  $16$ 
E)  $\frac { 1 } { 16 }$ 
A)  $- 1$ 
B)  $- 2$ 
C)  $- 3$ 
D)  $16$ 
E)  $\frac { 1 } { 16 }$

Question 7

Identify the graph of the function.
$f ( x ) = \left( \frac { 1 } { 2 } \right) ^ { 1 - x }$

Accepted Answer

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

Question 8

Determine whether the scatter plot below could best be modeled by a linear model, a quadratic model, an exponential model, a logarithmic model, or a logistic model.

Accepted Answer

A)  a linear model 
B)  a quadratic model 
C)  a logistic model 
D)  an exponential model 
E)  a logarithmic model 
A)  a linear model 
B)  a quadratic model 
C)  a logistic model 
D)  an exponential model 
E)  a logarithmic model

Question 9

Solve the logarithmic equation below algebraically.
$$\ln ( x - 6 ) = \ln ( x + 6 ) - \ln ( x - 4 )$$

Accepted Answer

A)  - 2 and 5 
B)  2 and 9 
C)  5 and 9 
D)  - 2 and 9 
E)  2 and 5 
A)  - 2 and 5 
B)  2 and 9 
C)  5 and 9 
D)  - 2 and 9 
E)  2 and 5

Question 10

Solve the logarithmic equation below algebraically.
$\ln ( x + 3 ) = \ln ( x + 1 ) - \ln ( x + 7 )$

Accepted Answer

A)  $1$ and $6$ 
B)  $- 5$ and $- 4$ 
C)  $- 4$ and $1$ 
D)  $- 4$ and $6$ 
E)  $- 5$ and $1$ 
A)  $1$ and $6$ 
B)  $- 5$ and $- 4$ 
C)  $- 4$ and $1$ 
D)  $- 4$ and $6$ 
E)  $- 5$ and $1$

Question 11

Solve $\ln x ^ { 2 } - \ln 3 = 0$ for $x$.

Accepted Answer

A)  9 
B)  $- \sqrt { 3 } , \sqrt { 3 }$ 
C)  $e ^ { 9 }$ 
D)  $e ^ { 3 / 2 }$ 
E)  no solution 
A)  9 
B)  $- \sqrt { 3 } , \sqrt { 3 }$ 
C)  $e ^ { 9 }$ 
D)  $e ^ { 3 / 2 }$ 
E)  no solution

Question 12

Solve the logarithmic equation below algebraically. Round your result to three decimal places.
$$\ln \sqrt { x + 6 } = 2$$

Accepted Answer

A)  $60.262$ 
B)  $97.681$ 
C)  $65.968$ 
D)  $67.927$ 
E)  $48.598$ 
A)  $60.262$ 
B)  $97.681$ 
C)  $65.968$ 
D)  $67.927$ 
E)  $48.598$

Question 13

Evaluate the function $f ( x ) = \frac { 1 } { 4 } \ln x \text { at } x = 14.67$ . Round to 3 decimal places. (You may use your calculator.)

Accepted Answer

A)  1.546 
B)  0.671 
C)  1.280 
D)  -0.347 
E)  undefined 
A)  1.546 
B)  0.671 
C)  1.280 
D)  -0.347 
E)  undefined

Question 14

Evaluate the logarithm $\log _ { 1 / 3 } 0.211$ using the change of base formula. Round to 3 decimal places.

Accepted Answer

A)  -1.556 
B)  1.709 
C)  0.706 
D)  1.416 
E)  -0.676 
A)  -1.556 
B)  1.709 
C)  0.706 
D)  1.416 
E)  -0.676

Question 15

Use the properties of logarithms to expand the expression as a sum, difference, and/or constant multiple of logarithms. (Assume all variables are positive.)
$\log _ { 4 } \frac { y } { 2 }$

Accepted Answer

A)  $2 \log _ { 4 } y$ 
B)  $y - \log _ { 4 } 2$ 
C)  $\log _ { 4 } y - 2$ 
D)  $\frac { \log _ { 4 } y } { 2 }$ 
E)  $\log _ { 4 } y - \log _ { 4 } 2$ 
A)  $2 \log _ { 4 } y$ 
B)  $y - \log _ { 4 } 2$ 
C)  $\log _ { 4 } y - 2$ 
D)  $\frac { \log _ { 4 } y } { 2 }$ 
E)  $\log _ { 4 } y - \log _ { 4 } 2$

Question 16

Simplify the expression below. $1 + e ^ { \ln x ^ { 6 } }$

Accepted Answer

A)  $1 + e ^ { 6 }$ 
B)  $1 + x ^ { 6 }$ 
C)  $1 + \ln 6$ 
D)  $\ln 7$ 
E)  $1 + 6 \ln x$ 
A)  $1 + e ^ { 6 }$ 
B)  $1 + x ^ { 6 }$ 
C)  $1 + \ln 6$ 
D)  $\ln 7$ 
E)  $1 + 6 \ln x$

Question 17

Solve the equation below for x. 
$\log _ { 5 } 5 ^ { 7 } = x$

Accepted Answer

A)  8 
B)  2 
C)  5 
D)  9 
E)  7 
A)  8 
B)  2 
C)  5 
D)  9 
E)  7

Question 18

Solve the exponential equation below algebraically. Round your result to three decimal places. $250 \left[ \frac { ( 1 + 0.03 ) ^ { x } } { 0.03 } \right] = 160,000$

Accepted Answer

A)  86.873 
B)  99.967 
C)  111.803 
D)  97.718 
E)  87.344 
A)  86.873 
B)  99.967 
C)  111.803 
D)  97.718 
E)  87.344

Question 19

Solve $\left( \frac { 1 } { 4 } \right) ^ { x } = 64$ for x.

Accepted Answer

A)  1 
B)  −1 
C)  −3 
D)  −4 
E)  no solution 
A)  1 
B)  −1 
C)  −3 
D)  −4 
E)  no solution

Question 20

Condense the expression below to the logarithm of a single quantity. $\frac { 3 } { 2 } \log _ { 7 } ( z + 5 )$

Accepted Answer

A)  $\log _ { 7 } ( \sqrt [ 3 ] { z } + 5 )$ 
B)  $\log _ { 7 } \left( \sqrt { z ^ { 3 } } + 5 \right)$ 
C)  $\log _ { 7 } \sqrt [ 3 ] { z + 5 }$ 
D)  $\log _ { 7 } \frac { 3 ( z + 5 ) } { 2 }$ 
E)  $\log _ { 7 } \sqrt { ( z + 5 ) ^ { 3 } }$ 
A)  $\log _ { 7 } ( \sqrt [ 3 ] { z } + 5 )$ 
B)  $\log _ { 7 } \left( \sqrt { z ^ { 3 } } + 5 \right)$ 
C)  $\log _ { 7 } \sqrt [ 3 ] { z + 5 }$ 
D)  $\log _ { 7 } \frac { 3 ( z + 5 ) } { 2 }$ 
E)  $\log _ { 7 } \sqrt { ( z + 5 ) ^ { 3 } }$

Identify the graph that represents the function. $y = 5 e ^ { - 2 ( x - 1 ) ^ { 2 } }$

Solve the logarithmic equation below algebraically. Round your result to three decimal places. $5 \log _ { 4 } ( x + 1 ) = 12$

Condense the expression $\frac { 1 } { 5 } \left[ \log _ { 4 } x + \log _ { 4 } 6 \right] - \left[ \log _ { 4 } y \right]$ to the logarithm of a single term.

Identify the graph that represents the function. $y = \ln \frac { 1 } { x + 1 }$

What is the value of the function $f ( x ) = 3.8 e ^ { - 1.5 x }$ at $x = 2.5 ?$ Round to 3 decimal places.

Evaluate the function $f ( x ) = \log _ { 4 } x$ at $x = \frac { 1 } { 16 }$ without using a calculator.

Identify the graph of the function. $f ( x ) = \left( \frac { 1 } { 2 } \right) ^ { 1 - x }$

Determine whether the scatter plot below could best be modeled by a linear model, a quadratic model, an exponential model, a logarithmic model, or a logistic model.

Solve the logarithmic equation below algebraically. $\ln ( x - 6 ) = \ln ( x + 6 ) - \ln ( x - 4 )$

Solve the logarithmic equation below algebraically. $\ln ( x + 3 ) = \ln ( x + 1 ) - \ln ( x + 7 )$

Solve $\ln x ^ { 2 } - \ln 3 = 0$ for $x$ .

Solve the logarithmic equation below algebraically. Round your result to three decimal places. $\ln \sqrt { x + 6 } = 2$

Evaluate the function $f ( x ) = \frac { 1 } { 4 } \ln x \text { at } x = 14.67$ . Round to 3 decimal places. (You may use your calculator.)

Evaluate the logarithm $\log _ { 1 / 3 } 0.211$ using the change of base formula. Round to 3 decimal places.

Use the properties of logarithms to expand the expression as a sum, difference, and/or constant multiple of logarithms. (Assume all variables are positive.) $\log _ { 4 } \frac { y } { 2 }$

Simplify the expression below. $1 + e ^ { \ln x ^ { 6 } }$

Solve the equation below for x. $\log _ { 5 } 5 ^ { 7 } = x$

Solve the exponential equation below algebraically. Round your result to three decimal places. $250 \left[ \frac { ( 1 + 0.03 ) ^ { x } } { 0.03 } \right] = 160,000$

Solve $\left( \frac { 1 } { 4 } \right) ^ { x } = 64$ for x.

Condense the expression below to the logarithm of a single quantity. $\frac { 3 } { 2 } \log _ { 7 } ( z + 5 )$

Functions and Their Graphs

Polynomial and Rational Functions

Trigonometric Functions

Analytic Trigonometry

Additional Topics in Trigonometry

Linear Systems and Matrices

Sequences, Series, and Probability

Topics in Analytic Geometry

Analytic Geometry in Three Dimensions

Limits and an Introduction to Calculus

Review of Graphs, Equations, and Inequalities

Filters

Exam 3: Exponential and Logarithmic Functions

Identify the graph that represents the function. y=5e−2(x−1)2y = 5 e ^ { - 2 ( x - 1 ) ^ { 2 } }y=5e−2(x−1)2

Solve the logarithmic equation below algebraically. Round your result to three decimal places. 5log⁡4(x+1)=125 \log _ { 4 } ( x + 1 ) = 125log4​(x+1)=12

Condense the expression 15[log⁡4x+log⁡46]−[log⁡4y]\frac { 1 } { 5 } \left[ \log _ { 4 } x + \log _ { 4 } 6 \right] - \left[ \log _ { 4 } y \right]51​[log4​x+log4​6]−[log4​y] to the logarithm of a single term.

Identify the graph that represents the function. y=ln⁡1x+1y = \ln \frac { 1 } { x + 1 }y=lnx+11​

What is the value of the function f(x)=3.8e−1.5xf ( x ) = 3.8 e ^ { - 1.5 x }f(x)=3.8e−1.5x at x=2.5?x = 2.5 ?x=2.5? Round to 3 decimal places.

Evaluate the function f(x)=log⁡4xf ( x ) = \log _ { 4 } xf(x)=log4​x at x=116x = \frac { 1 } { 16 }x=161​ without using a calculator.

Identify the graph of the function. f(x)=(12)1−xf ( x ) = \left( \frac { 1 } { 2 } \right) ^ { 1 - x }f(x)=(21​)1−x

Determine whether the scatter plot below could best be modeled by a linear model, a quadratic model, an exponential model, a logarithmic model, or a logistic model.

Solve the logarithmic equation below algebraically. ln⁡(x−6)=ln⁡(x+6)−ln⁡(x−4)\ln ( x - 6 ) = \ln ( x + 6 ) - \ln ( x - 4 )ln(x−6)=ln(x+6)−ln(x−4)

Solve the logarithmic equation below algebraically. ln⁡(x+3)=ln⁡(x+1)−ln⁡(x+7)\ln ( x + 3 ) = \ln ( x + 1 ) - \ln ( x + 7 )ln(x+3)=ln(x+1)−ln(x+7)

Solve ln⁡x2−ln⁡3=0\ln x ^ { 2 } - \ln 3 = 0lnx2−ln3=0 for xxx .

Solve the logarithmic equation below algebraically. Round your result to three decimal places. ln⁡x+6=2\ln \sqrt { x + 6 } = 2lnx+6​=2

Evaluate the function f(x)=14ln⁡x at x=14.67f ( x ) = \frac { 1 } { 4 } \ln x \text { at } x = 14.67f(x)=41​lnx at x=14.67 . Round to 3 decimal places. (You may use your calculator.)

Evaluate the logarithm log⁡1/30.211\log _ { 1 / 3 } 0.211log1/3​0.211 using the change of base formula. Round to 3 decimal places.

Use the properties of logarithms to expand the expression as a sum, difference, and/or constant multiple of logarithms. (Assume all variables are positive.) log⁡4y2\log _ { 4 } \frac { y } { 2 }log4​2y​

Simplify the expression below. 1+eln⁡x61 + e ^ { \ln x ^ { 6 } }1+elnx6

Solve the equation below for x. log⁡557=x\log _ { 5 } 5 ^ { 7 } = xlog5​57=x

Solve the exponential equation below algebraically. Round your result to three decimal places. 250[(1+0.03)x0.03]=160,000250 \left[ \frac { ( 1 + 0.03 ) ^ { x } } { 0.03 } \right] = 160,000250[0.03(1+0.03)x​]=160,000

Solve (14)x=64\left( \frac { 1 } { 4 } \right) ^ { x } = 64(41​)x=64 for x.

Condense the expression below to the logarithm of a single quantity. 32log⁡7(z+5)\frac { 3 } { 2 } \log _ { 7 } ( z + 5 )23​log7​(z+5)

Functions and Their Graphs

Polynomial and Rational Functions

Trigonometric Functions

Analytic Trigonometry

Additional Topics in Trigonometry

Linear Systems and Matrices

Sequences, Series, and Probability

Topics in Analytic Geometry

Analytic Geometry in Three Dimensions

Limits and an Introduction to Calculus

Review of Graphs, Equations, and Inequalities

Filters

Identify the graph that represents the function. $y = 5 e ^ { - 2 ( x - 1 ) ^ { 2 } }$

Solve the logarithmic equation below algebraically. Round your result to three decimal places. $5 \log _ { 4 } ( x + 1 ) = 12$

Condense the expression $\frac { 1 } { 5 } \left[ \log _ { 4 } x + \log _ { 4 } 6 \right] - \left[ \log _ { 4 } y \right]$ to the logarithm of a single term.

Identify the graph that represents the function. $y = \ln \frac { 1 } { x + 1 }$

What is the value of the function $f ( x ) = 3.8 e ^ { - 1.5 x }$ at $x = 2.5 ?$ Round to 3 decimal places.

Evaluate the function $f ( x ) = \log _ { 4 } x$ at $x = \frac { 1 } { 16 }$ without using a calculator.

Identify the graph of the function. $f ( x ) = \left( \frac { 1 } { 2 } \right) ^ { 1 - x }$

Solve the logarithmic equation below algebraically. $\ln ( x - 6 ) = \ln ( x + 6 ) - \ln ( x - 4 )$

Solve the logarithmic equation below algebraically. $\ln ( x + 3 ) = \ln ( x + 1 ) - \ln ( x + 7 )$

Solve $\ln x ^ { 2 } - \ln 3 = 0$ for $x$ .

Solve the logarithmic equation below algebraically. Round your result to three decimal places. $\ln \sqrt { x + 6 } = 2$

Evaluate the function $f ( x ) = \frac { 1 } { 4 } \ln x \text { at } x = 14.67$ . Round to 3 decimal places. (You may use your calculator.)

Evaluate the logarithm $\log _ { 1 / 3 } 0.211$ using the change of base formula. Round to 3 decimal places.

Use the properties of logarithms to expand the expression as a sum, difference, and/or constant multiple of logarithms. (Assume all variables are positive.) $\log _ { 4 } \frac { y } { 2 }$

Simplify the expression below. $1 + e ^ { \ln x ^ { 6 } }$

Solve the equation below for x. $\log _ { 5 } 5 ^ { 7 } = x$

Solve the exponential equation below algebraically. Round your result to three decimal places. $250 \left[ \frac { ( 1 + 0.03 ) ^ { x } } { 0.03 } \right] = 160,000$

Solve $\left( \frac { 1 } { 4 } \right) ^ { x } = 64$ for x.

Condense the expression below to the logarithm of a single quantity. $\frac { 3 } { 2 } \log _ { 7 } ( z + 5 )$