Question 1

Condense the expression below to the logarithm of a single quantity.
$$5 [ \ln x - \ln ( x + 2 ) - \ln ( x - 2 ) ]$$

Accepted Answer

A)  $\ln \left( x ^ { 5 } - \left( x ^ { 2 } - 4 \right) ^ { 5 } \right)$ 
B)  $\quad \ln \left( x ^ { 5 } - ( x + 2 ) ^ { 5 } - ( x - 2 ) ^ { 5 } \right)$ 
C)  $\ln \frac { x ^ { 5 } } { x ^ { 2 } - 4 }$ 
D)  $\ln \left( \left( \frac { x } { x ^ { 2 } - 4 } \right) ^ { 5 } \right)$ 
E)  $\quad \ln \frac { x } { \left( x ^ { 2 } - 4 \right) ^ { 5 } }$ 
A)  $\ln \left( x ^ { 5 } - \left( x ^ { 2 } - 4 \right) ^ { 5 } \right)$ 
B)  $\quad \ln \left( x ^ { 5 } - ( x + 2 ) ^ { 5 } - ( x - 2 ) ^ { 5 } \right)$ 
C)  $\ln \frac { x ^ { 5 } } { x ^ { 2 } - 4 }$ 
D)  $\ln \left( \left( \frac { x } { x ^ { 2 } - 4 } \right) ^ { 5 } \right)$ 
E)  $\quad \ln \frac { x } { \left( x ^ { 2 } - 4 \right) ^ { 5 } }$

Question 2

Evaluate the function $f ( x ) = \frac { 1 } { 4 } \ln x$ 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 3

Identify the value of the function $f ( x ) = \log _ { 10 } x$ at $x = 715$. Round to 3 decimal places.

Accepted Answer

A)  $2.854$ 
B)  $3.354$ 
C)  $3.854$ 
D)  $4.354$ 
E)  $6.572$ l 
A)  $2.854$ 
B)  $3.354$ 
C)  $3.854$ 
D)  $4.354$ 
E)  $6.572$ l

Question 4

Evaluate the logarithm $\log _ { 1 / 3 } 0.113$ using the change of base formula. Round to 3 decimal places.

Accepted Answer

A)  $- 2.180$ 
B)  $2.395$ 
C)  $0.504$ 
D)  $1.985$ 
E)  $- 0.947$ 
A)  $- 2.180$ 
B)  $2.395$ 
C)  $0.504$ 
D)  $1.985$ 
E)  $- 0.947$

Question 5

Find the exact value of $\ln e ^ { 1.50 } - \ln \sqrt { e }$ without using a calculator.

Accepted Answer

A)  $0.75$ 
B)  3 
C)  1 
D)  2 
E)  $1.5$ 
A)  $0.75$ 
B)  3 
C)  1 
D)  2 
E)  $1.5$

Question 6

Approximate the solution of $9 e ^ { x + 3 } = 18$ to 3 decimal places. (You may use a graphing utility.)

Accepted Answer

A)  $- 0.803$ 
B)  $4.389$ 
C)  $- 2.699$ 
D)  $3.693$ 
E)  $- 2.307$ 
A)  $- 0.803$ 
B)  $4.389$ 
C)  $- 2.699$ 
D)  $3.693$ 
E)  $- 2.307$

Question 7

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 8

Identify the $x$-intercept of the function $y = 3 + \log _ { 4 } x$.

Accepted Answer

A)  64 
B)  $\frac { 1 } { 64 }$ 
C)  $- 3$ 
D)  12 
E)  The function has no $x$-intercept. 
A)  64 
B)  $\frac { 1 } { 64 }$ 
C)  $- 3$ 
D)  12 
E)  The function has no $x$-intercept.

Question 9

Solve the logarithmic equation below algebraically. Round your result to three decimal places.
$\ln \sqrt { x - 4 } = 2$

Accepted Answer

A)  $38.489$ 
B)  $28.421$ 
C)  $3.668$ 
D)  $74.354$ 
E)  $58.598$ 
A)  $38.489$ 
B)  $28.421$ 
C)  $3.668$ 
D)  $74.354$ 
E)  $58.598$

Question 10

Solve the logarithmic equation below algebraically.
$$\log _ { 6 } ( 2 x + 4 ) = \log _ { 6 } ( 5 x + 1 )$$

Accepted Answer

A)  3 
B)  $- 2$ 
C)  $- 4$ 
D)  2 
E)  1 
A)  3 
B)  $- 2$ 
C)  $- 4$ 
D)  2 
E)  1

Question 11

Solve the equation $f ( x ) = g ( x )$ algebraically.
$$\begin{array} { l } 
f ( x ) = \ln e ^ { 3 x - 9 } \
g ( x ) = x - 5
\end{array}$$

Accepted Answer

A)  0 
B)  $- 1$ 
C)  2 
D)  5 
E)  1 
A)  0 
B)  $- 1$ 
C)  2 
D)  5 
E)  1

Question 12

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 13

Match the function $y = 2 e ^ { - x }$ with its graph.
Graph I:
 
Graph II:
 
Graph III:
 
Graph IV:

Graph V:

Accepted Answer

A)  Graph II 
B)  Graph IV 
C)  Graph III 
D)  Graph V 
E)  Graph I 
A)  Graph II 
B)  Graph IV 
C)  Graph III 
D)  Graph V 
E)  Graph I

Question 14

Solve the equation below algebraically. Round your result to three decimal places.
$$\frac { 3 + \ln x } { x ^ { 2 } } = 0$$

Accepted Answer

A)  $- 1.876$ 
B)  $1.061$ 
C)  $- 1.390$ 
D)  $- 2.512$ 
E)  $0.050$ 
A)  $- 1.876$ 
B)  $1.061$ 
C)  $- 1.390$ 
D)  $- 2.512$ 
E)  $0.050$

Question 15

Simplify the expression $\log _ { 3 } \left( \frac { 1 } { 27 } \right) ^ { 3 }$.

Accepted Answer

A)  3 
B)  $- 9$ 
C)  0 
D)  $- 81$ 
E)  The expression cannot be simplified. 
A)  3 
B)  $- 9$ 
C)  0 
D)  $- 81$ 
E)  The expression cannot be simplified.

Question 16

Solve the equation $f ( x ) = g ( x )$ algebraically.
$$\begin{array} { l } 
f ( x ) = \ln e ^ { 2 x + 2 } \
g ( x ) = 3 x + 6
\end{array}$$

Accepted Answer

A)  5 
B)  4 
C)  $- 4$ 
D)  $- 5$ 
E)  2 
A)  5 
B)  4 
C)  $- 4$ 
D)  $- 5$ 
E)  2

Question 17

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 18

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 19

Simplify the expression $\log _ { 5 } 150$.

Accepted Answer

A)  $2 + \log _ { 5 } 6$ 
B)  $30 \log _ { 5 } 2$ 
C)  6 
D)  $2 \log _ { 5 } 6$ 
E)  The expression cannot be simplified. 
A)  $2 + \log _ { 5 } 6$ 
B)  $30 \log _ { 5 } 2$ 
C)  6 
D)  $2 \log _ { 5 } 6$ 
E)  The expression cannot be simplified.

Question 20

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

Accepted Answer

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

Condense the expression below to the logarithm of a single quantity. $5 [ \ln x - \ln ( x + 2 ) - \ln ( x - 2 ) ]$

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

Identify the value of the function $f ( x ) = \log _ { 10 } x$ at $x = 715$ . Round to 3 decimal places.

Evaluate the logarithm $\log _ { 1 / 3 } 0.113$ using the change of base formula. Round to 3 decimal places.

Find the exact value of $\ln e ^ { 1.50 } - \ln \sqrt { e }$ without using a calculator.

Approximate the solution of $9 e ^ { x + 3 } = 18$ to 3 decimal places. (You may use a graphing utility.)

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

Identify the $x$ -intercept of the function $y = 3 + \log _ { 4 } x$ .

Solve the logarithmic equation below algebraically. Round your result to three decimal places. $\ln \sqrt { x - 4 } = 2$

Solve the logarithmic equation below algebraically. $\log _ { 6 } ( 2 x + 4 ) = \log _ { 6 } ( 5 x + 1 )$

Solve the equation $f ( x ) = g ( x )$ algebraically. f(x)= g(x)=x-5

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

Solve the equation below algebraically. Round your result to three decimal places. $\frac { 3 + \ln x } { x ^ { 2 } } = 0$

Simplify the expression $\log _ { 3 } \left( \frac { 1 } { 27 } \right) ^ { 3 }$ .

Solve the equation $f ( x ) = g ( x )$ algebraically. f(x)= g(x)=3x+6

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

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.

Simplify the expression $\log _ { 5 } 150$ .

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

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

Filters

Exam 3: Exponential and Logarithmic Functions

Condense the expression below to the logarithm of a single quantity. 5[ln⁡x−ln⁡(x+2)−ln⁡(x−2)]5 [ \ln x - \ln ( x + 2 ) - \ln ( x - 2 ) ]5[lnx−ln(x+2)−ln(x−2)]

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

Identify the value of the function f(x)=log⁡10xf ( x ) = \log _ { 10 } xf(x)=log10​x at x=715x = 715x=715 . Round to 3 decimal places.

Evaluate the logarithm log⁡1/30.113\log _ { 1 / 3 } 0.113log1/3​0.113 using the change of base formula. Round to 3 decimal places.

Find the exact value of ln⁡e1.50−ln⁡e\ln e ^ { 1.50 } - \ln \sqrt { e }lne1.50−lne​ without using a calculator.

Approximate the solution of 9ex+3=189 e ^ { x + 3 } = 189ex+3=18 to 3 decimal places. (You may use a graphing utility.)

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

Identify the xxx -intercept of the function y=3+log⁡4xy = 3 + \log _ { 4 } xy=3+log4​x .

Solve the logarithmic equation below algebraically. Round your result to three decimal places. ln⁡x−4=2\ln \sqrt { x - 4 } = 2lnx−4​=2

Solve the logarithmic equation below algebraically. log⁡6(2x+4)=log⁡6(5x+1)\log _ { 6 } ( 2 x + 4 ) = \log _ { 6 } ( 5 x + 1 )log6​(2x+4)=log6​(5x+1)

Solve the equation f(x)=g(x)f ( x ) = g ( x )f(x)=g(x) algebraically. f(x)= g(x)=x-5

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.

Match the function y=2e−xy = 2 e ^ { - x }y=2e−x with its graph. Graph I: Graph II: Graph III: Graph IV: Graph V:

Solve the equation below algebraically. Round your result to three decimal places. 3+ln⁡xx2=0\frac { 3 + \ln x } { x ^ { 2 } } = 0x23+lnx​=0

Simplify the expression log⁡3(127)3\log _ { 3 } \left( \frac { 1 } { 27 } \right) ^ { 3 }log3​(271​)3 .

Solve the equation f(x)=g(x)f ( x ) = g ( x )f(x)=g(x) algebraically. f(x)= g(x)=3x+6

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

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.

Simplify the expression log⁡5150\log _ { 5 } 150log5​150 .

Identify the graph of the function. f(x)=(12)x2f ( x ) = \left( \frac { 1 } { 2 } \right) ^ { x ^ { 2 } }f(x)=(21​)x2

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

Filters

Condense the expression below to the logarithm of a single quantity. $5 [ \ln x - \ln ( x + 2 ) - \ln ( x - 2 ) ]$

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

Identify the value of the function $f ( x ) = \log _ { 10 } x$ at $x = 715$ . Round to 3 decimal places.

Evaluate the logarithm $\log _ { 1 / 3 } 0.113$ using the change of base formula. Round to 3 decimal places.

Find the exact value of $\ln e ^ { 1.50 } - \ln \sqrt { e }$ without using a calculator.

Approximate the solution of $9 e ^ { x + 3 } = 18$ to 3 decimal places. (You may use a graphing utility.)

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

Identify the $x$ -intercept of the function $y = 3 + \log _ { 4 } x$ .

Solve the logarithmic equation below algebraically. Round your result to three decimal places. $\ln \sqrt { x - 4 } = 2$

Solve the logarithmic equation below algebraically. $\log _ { 6 } ( 2 x + 4 ) = \log _ { 6 } ( 5 x + 1 )$

Solve the equation $f ( x ) = g ( x )$ algebraically. f(x)= g(x)=x-5

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

Solve the equation below algebraically. Round your result to three decimal places. $\frac { 3 + \ln x } { x ^ { 2 } } = 0$

Simplify the expression $\log _ { 3 } \left( \frac { 1 } { 27 } \right) ^ { 3 }$ .

Solve the equation $f ( x ) = g ( x )$ algebraically. f(x)= g(x)=3x+6

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

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.

Simplify the expression $\log _ { 5 } 150$ .

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