Question 1

Evaluate $f ( x ) = \log x$ at the indicated value of x.Round your result to three decimal places. $x = \frac { 3 } { 2 }$

Accepted Answer

A) 5.682 
B) 1.5 
C) -0.176 
D) -5.682 
E) 0.176 
A) 5.682 
B) 1.5 
C) -0.176 
D) -5.682 
E) 0.176

Question 2

Evaluate the function $f ( x ) = 1.3 ^ { x }$ at $x = 2.7$ .Round to 3 decimal places.

Accepted Answer

A) 1.690 
B) 2.031 
C) 3.637 
D) 9.477 
E) 3.510 
A) 1.690 
B) 2.031 
C) 3.637 
D) 9.477 
E) 3.510

Question 3

Condense the expression 7(log x - log y) to the logarithm of a single term.

Accepted Answer

A)  $\log \left( \frac { x } { y } \right) ^ { 7 }$ 
B)  $\log \frac { 7 x } { 7 y }$ 
C)  $\log \frac { x ^ { 7 } } { y }$ 
D)  $\log \frac { x ^ { 7 } } { \sqrt [ 7 ] { y } }$ 
E) 7(log x - log y) 
A)  $\log \left( \frac { x } { y } \right) ^ { 7 }$ 
B)  $\log \frac { 7 x } { 7 y }$ 
C)  $\log \frac { x ^ { 7 } } { y }$ 
D)  $\log \frac { x ^ { 7 } } { \sqrt [ 7 ] { y } }$ 
E) 7(log x - log y)

Question 4

Write the logarithmic equation in exponential form.  $\log _ { 15 } \frac { 1 } { 3375 } = - 3$

Accepted Answer

A)  $3375 ^ { - 3 } = \frac { 1 } { 15 }$ 
B)  $15 ^ { - 3 } = - 3375$ 
C)  $15 ^ { - 3 } = 3375$ 
D)  $15 ^ { - 3 } = - \frac { 1 } { 3375 }$ 
E)  $15 ^ { - 3 } = \frac { 1 } { 3375 }$ 
A)  $3375 ^ { - 3 } = \frac { 1 } { 15 }$ 
B)  $15 ^ { - 3 } = - 3375$ 
C)  $15 ^ { - 3 } = 3375$ 
D)  $15 ^ { - 3 } = - \frac { 1 } { 3375 }$ 
E)  $15 ^ { - 3 } = \frac { 1 } { 3375 }$

Question 5

Solve for x.Approximate the result to three decimal places.  $\log _ { 7 } x = \frac { 1 } { 2 }$

Accepted Answer

A)  $\sqrt { 7 } \approx 2.828$ 
B)  $\sqrt { 7 } = 2.646$ 
C)  $\sqrt { 7 } \approx - 2.646$ 
D)  $\sqrt { 7 } \approx 2.646$ 
E)  $\frac { \sqrt { 7 } } { 7 } \approx 2.646$ 
A)  $\sqrt { 7 } \approx 2.828$ 
B)  $\sqrt { 7 } = 2.646$ 
C)  $\sqrt { 7 } \approx - 2.646$ 
D)  $\sqrt { 7 } \approx 2.646$ 
E)  $\frac { \sqrt { 7 } } { 7 } \approx 2.646$

Question 6

Sketch the graph of the function.  $f ( x ) = 2 - 2 ^ { x }$

Accepted Answer

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

Question 7

Find the exact value of $\log _ { 7 } \sqrt [ 3 ] { 49 }$ without using a calculator.

Accepted Answer

A)  $\frac { 49 } { 3 }$ 
B)  $\frac { 3 } { 49 }$ 
C)  $\frac { 14 } { 3 }$ 
D)  $\frac { 2 } { 3 }$ 
E) -1 
A)  $\frac { 49 } { 3 }$ 
B)  $\frac { 3 } { 49 }$ 
C)  $\frac { 14 } { 3 }$ 
D)  $\frac { 2 } { 3 }$ 
E) -1

Question 8

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.What is $\left[ \mathrm { H } ^ { + } \right]$ if the $\mathrm { pH } = 3.8$

Accepted Answer

A) 3.800 
B)  $6.31 \times 10 ^ { - 4 }$ 
C)  $6.31 \times 10 ^ { - 3 }$ 
D)  $1.58 \times 10 ^ { - 3 }$ 
E)  $1.58 \times 10 ^ { - 4 }$ 
A) 3.800 
B)  $6.31 \times 10 ^ { - 4 }$ 
C)  $6.31 \times 10 ^ { - 3 }$ 
D)  $1.58 \times 10 ^ { - 3 }$ 
E)  $1.58 \times 10 ^ { - 4 }$

Question 9

Evaluate the logarithm using the change-of-base formula.Round your result to three decimal places.
 $\log _ { \frac { 1 } { 3 } } 6$

Accepted Answer

A) -0.631 
B) 2.369 
C) 0.369 
D) -1.631 
E) 1.369 
A) -0.631 
B) 2.369 
C) 0.369 
D) -1.631 
E) 1.369

Question 10

Identify the value of the function $f ( x ) = \log _ { 10 } x$ at $x = 915$ .Round to 3 decimal places.

Accepted Answer

A) 6.819 
B) 3.961 
C) 2.961 
D) 4.461 
E) 3.461 
A) 6.819 
B) 3.961 
C) 2.961 
D) 4.461 
E) 3.461

Question 11

Write the equation $6 ^ { 5 } = 7,776$ in logarithmic form.

Accepted Answer

A)  $\log _ { 6 } 7,776 = 5$ 
B)  $\log _ { 5 } 6 = 7,776$ 
C)  $\log _ { 7,776 } 6 = 5$ 
D)  $\log _ { 6 } 5 = 7,776$ 
E)  $\log _ { 5 } 7,776 = 6$ 
A)  $\log _ { 6 } 7,776 = 5$ 
B)  $\log _ { 5 } 6 = 7,776$ 
C)  $\log _ { 7,776 } 6 = 5$ 
D)  $\log _ { 6 } 5 = 7,776$ 
E)  $\log _ { 5 } 7,776 = 6$

Question 12

Write the exponential equation in logarithmic form. $2 ^ { - 2 } = \frac { 1 } { 4 }$

Accepted Answer

A)  $\log _ { 4 } \frac { 1 } { 2 } = - 2$ 
B)  $\log _ { 2 } \frac { 1 } { 4 } = 2$ 
C)  $\log _ { 2 } 4 = 2$ 
D)  $\log _ { 2 } \frac { 1 } { 4 } = - 2$ 
E)  $\log _ { 2 } 4 = - 2$ 
A)  $\log _ { 4 } \frac { 1 } { 2 } = - 2$ 
B)  $\log _ { 2 } \frac { 1 } { 4 } = 2$ 
C)  $\log _ { 2 } 4 = 2$ 
D)  $\log _ { 2 } \frac { 1 } { 4 } = - 2$ 
E)  $\log _ { 2 } 4 = - 2$

Question 13

Use the One-to-One Property to solve the equation for x.  $e ^ { x ^ { 2 } - 4 } = e ^ { 3 x }$

Accepted Answer

A)  $x = - 4$ 
B)  $x = 3$ 
C)  $x = 4 , - 1$ 
D)  $x = - 4 , - 1$ 
E)  $x = - 4,1$ 
A)  $x = - 4$ 
B)  $x = 3$ 
C)  $x = 4 , - 1$ 
D)  $x = - 4 , - 1$ 
E)  $x = - 4,1$

Question 14

Graph the function using translations.  $f ( x ) = 4 ^ { x + 1 } + 1$

Accepted Answer

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

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 5x4y

Accepted Answer

A) log 5 × 4log x × log y 
B) log 5 + 4log x - log y 
C) log 5 + log x + 4log y 
D) log 5 + 4log x + log y 
E)  $\frac { \log 5 } { 4 ( \log x + \log y ) }$ 
A) log 5 × 4log x × log y 
B) log 5 + 4log x - log y 
C) log 5 + log x + 4log y 
D) log 5 + 4log x + log y 
E)  $\frac { \log 5 } { 4 ( \log x + \log y ) }$

Question 16

Solve for x.   $\ln x - \ln 5 = 0$

Accepted Answer

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

Question 17

Write the exponential equation in logarithmic form.   $e ^ { 1 / 2 } = 1.649$

Accepted Answer

A)  $\ln 1.649 \ldots = 2$ 
B)  $\ln 1.649 \ldots = - 2$ 
C)  $\ln 1.649 \ldots = \frac { 1 } { 2 }$ 
D)  $\ln 2 \ldots = 1.649$ 
E)  $\ln 1.649 \ldots = - \frac { 1 } { 2 }$ 
A)  $\ln 1.649 \ldots = 2$ 
B)  $\ln 1.649 \ldots = - 2$ 
C)  $\ln 1.649 \ldots = \frac { 1 } { 2 }$ 
D)  $\ln 2 \ldots = 1.649$ 
E)  $\ln 1.649 \ldots = - \frac { 1 } { 2 }$

Question 18

What is the value of the function $f ( x ) = 125 e ^ { 0.8 x }$ at $x = 2.3$ ? Round to 3 decimal places.

Accepted Answer

A) 278.193 
B) 127.226 
C) 74.820 
D) 787.067 
E) 8647.887 
A) 278.193 
B) 127.226 
C) 74.820 
D) 787.067 
E) 8647.887

Question 19

Use the properties of logarithms to rewrite and simplify the logarithmic expression. ​
Ln (3e4)
​

Accepted Answer

A) ln 4 
B) ln 3 + 4 
C) ln 4 + 3 
D) ln 7 
E) ln 3 
A) ln 4 
B) ln 3 + 4 
C) ln 4 + 3 
D) ln 7 
E) ln 3

Question 20

The value V (in millions of dollars) of a famous painting can be modeled by $V = 10 e ^ { i t }$ where t represents the year, with t = 0 corresponding to 2000.In 2008, the same painting was sold for $65 million.Predict the value of the painting in 2018.(Round your answer to two decimal places.)

Accepted Answer

A) $674.61 million 
B) $874.61 million 
C) $474.61 million 
D) $774.61 million 
E) $574.61 million 
A) $674.61 million 
B) $874.61 million 
C) $474.61 million 
D) $774.61 million 
E) $574.61 million

Evaluate $f ( x ) = \log x$ at the indicated value of x.Round your result to three decimal places. $x = \frac { 3 } { 2 }$

Evaluate the function $f ( x ) = 1.3 ^ { x }$ at $x = 2.7$ .Round to 3 decimal places.

Condense the expression 7(log x - log y) to the logarithm of a single term.

Write the logarithmic equation in exponential form. $\log _ { 15 } \frac { 1 } { 3375 } = - 3$

Solve for x.Approximate the result to three decimal places. $\log _ { 7 } x = \frac { 1 } { 2 }$

Sketch the graph of the function. $f ( x ) = 2 - 2 ^ { x }$

Find the exact value of $\log _ { 7 } \sqrt [ 3 ] { 49 }$ without using a calculator.

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.What is $\left[ \mathrm { H } ^ { + } \right]$ if the $\mathrm { pH } = 3.8$

Evaluate the logarithm using the change-of-base formula.Round your result to three decimal places. $\log _ { \frac { 1 } { 3 } } 6$

Identify the value of the function $f ( x ) = \log _ { 10 } x$ at $x = 915$ .Round to 3 decimal places.

Write the equation $6 ^ { 5 } = 7,776$ in logarithmic form.

Write the exponential equation in logarithmic form. $2 ^ { - 2 } = \frac { 1 } { 4 }$

Use the One-to-One Property to solve the equation for x. $e ^ { x ^ { 2 } - 4 } = e ^ { 3 x }$

Graph the function using translations. $f ( x ) = 4 ^ { x + 1 } + 1$

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 5x⁴y

Solve for x. $\ln x - \ln 5 = 0$

Write the exponential equation in logarithmic form. $e ^ { 1 / 2 } = 1.649$

What is the value of the function $f ( x ) = 125 e ^ { 0.8 x }$ at $x = 2.3$ ? Round to 3 decimal places.

Use the properties of logarithms to rewrite and simplify the logarithmic expression. Ln (3e⁴)

The value V (in millions of dollars) of a famous painting can be modeled by $V = 10 e ^ { i t }$ where t represents the year, with t = 0 corresponding to 2000.In 2008, the same painting was sold for $65 million.Predict the value of the painting in 2018.(Round your answer to two decimal places.)

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 f(x)=log⁡xf ( x ) = \log xf(x)=logx at the indicated value of x.Round your result to three decimal places. x=32x = \frac { 3 } { 2 }x=23​

Evaluate the function f(x)=1.3xf ( x ) = 1.3 ^ { x }f(x)=1.3x at x=2.7x = 2.7x=2.7 .Round to 3 decimal places.

Condense the expression 7(log x - log y) to the logarithm of a single term.

Write the logarithmic equation in exponential form. log⁡1513375=−3\log _ { 15 } \frac { 1 } { 3375 } = - 3log15​33751​=−3

Solve for x.Approximate the result to three decimal places. log⁡7x=12\log _ { 7 } x = \frac { 1 } { 2 }log7​x=21​

Sketch the graph of the function. f(x)=2−2xf ( x ) = 2 - 2 ^ { x }f(x)=2−2x

Find the exact value of log⁡7493\log _ { 7 } \sqrt [ 3 ] { 49 }log7​349​ without using a calculator.

Evaluate the logarithm using the change-of-base formula.Round your result to three decimal places. log⁡136\log _ { \frac { 1 } { 3 } } 6log31​​6

Identify the value of the function f(x)=log⁡10xf ( x ) = \log _ { 10 } xf(x)=log10​x at x=915x = 915x=915 .Round to 3 decimal places.

Write the equation 65=7,7766 ^ { 5 } = 7,77665=7,776 in logarithmic form.

Write the exponential equation in logarithmic form. 2−2=142 ^ { - 2 } = \frac { 1 } { 4 }2−2=41​

Use the One-to-One Property to solve the equation for x. ex2−4=e3xe ^ { x ^ { 2 } - 4 } = e ^ { 3 x }ex2−4=e3x

Graph the function using translations. f(x)=4x+1+1f ( x ) = 4 ^ { x + 1 } + 1f(x)=4x+1+1

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 5x4y

Solve for x. ln⁡x−ln⁡5=0\ln x - \ln 5 = 0lnx−ln5=0

Write the exponential equation in logarithmic form. e1/2=1.649e ^ { 1 / 2 } = 1.649e1/2=1.649

What is the value of the function f(x)=125e0.8xf ( x ) = 125 e ^ { 0.8 x }f(x)=125e0.8x at x=2.3x = 2.3x=2.3 ? Round to 3 decimal places.

Use the properties of logarithms to rewrite and simplify the logarithmic expression. ​ Ln (3e4) ​

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 $f ( x ) = \log x$ at the indicated value of x.Round your result to three decimal places. $x = \frac { 3 } { 2 }$

Evaluate the function $f ( x ) = 1.3 ^ { x }$ at $x = 2.7$ .Round to 3 decimal places.

Write the logarithmic equation in exponential form. $\log _ { 15 } \frac { 1 } { 3375 } = - 3$

Solve for x.Approximate the result to three decimal places. $\log _ { 7 } x = \frac { 1 } { 2 }$

Sketch the graph of the function. $f ( x ) = 2 - 2 ^ { x }$

Find the exact value of $\log _ { 7 } \sqrt [ 3 ] { 49 }$ without using a calculator.

Evaluate the logarithm using the change-of-base formula.Round your result to three decimal places. $\log _ { \frac { 1 } { 3 } } 6$

Identify the value of the function $f ( x ) = \log _ { 10 } x$ at $x = 915$ .Round to 3 decimal places.

Write the equation $6 ^ { 5 } = 7,776$ in logarithmic form.

Write the exponential equation in logarithmic form. $2 ^ { - 2 } = \frac { 1 } { 4 }$

Use the One-to-One Property to solve the equation for x. $e ^ { x ^ { 2 } - 4 } = e ^ { 3 x }$

Graph the function using translations. $f ( x ) = 4 ^ { x + 1 } + 1$

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 5x⁴y

Solve for x. $\ln x - \ln 5 = 0$

Write the exponential equation in logarithmic form. $e ^ { 1 / 2 } = 1.649$

What is the value of the function $f ( x ) = 125 e ^ { 0.8 x }$ at $x = 2.3$ ? Round to 3 decimal places.

Use the properties of logarithms to rewrite and simplify the logarithmic expression. Ln (3e⁴)