Question 1

Identify the value of the function $f ( x ) = \log _ { 10 } x$ at $x = 315$ .Round to 3 decimal places.

Accepted Answer

A) 2.498 
B) 2.998 
C) 3.498 
D) 3.998 
E) 5.753 
A) 2.498 
B) 2.998 
C) 3.498 
D) 3.998 
E) 5.753

Question 2

Condense the expression $\frac { 1 } { 3 } \left[ \log _ { 6 } x + \log _ { 6 } 7 \right] - \left[ \log _ { 6 } y \right]$ to the logarithm of a single term.

Accepted Answer

A)  $\log _ { 6 } \frac { ( 7 x ) ^ { 3 } } { y }$ 
B)  $\log _ { 6 } \frac { \sqrt [ 3 ] { 7 x } } { y }$ 
C)  $\log _ { 6 } \sqrt [ 3 ] { \frac { 7 x } { y } }$ 
D)  $\log _ { 6 } \sqrt [ 3 ] { 7 x } - \log _ { 6 } y$ 
E)  $\log _ { 6 } \frac { 7 x } { 3 y }$ 
A)  $\log _ { 6 } \frac { ( 7 x ) ^ { 3 } } { y }$ 
B)  $\log _ { 6 } \frac { \sqrt [ 3 ] { 7 x } } { y }$ 
C)  $\log _ { 6 } \sqrt [ 3 ] { \frac { 7 x } { y } }$ 
D)  $\log _ { 6 } \sqrt [ 3 ] { 7 x } - \log _ { 6 } y$ 
E)  $\log _ { 6 } \frac { 7 x } { 3 y }$

Question 3

Assume that x is a positive number.Use the properties of logarithms to write the expression   
Logb (x + 8) - logb x as the logarithm of one quantity.

Accepted Answer

A)  $\log _ { b } \frac { x ^ { 2 } + 8 } { x }$ 
B)  $\log _ { b } \frac { x + 8 } { x }$ 
C)  $\log _ { b } \frac { x - 8 } { x }$ 
D)  $\log _ { b } \frac { x ^ { 2 } + 8 } { 8 }$ 
E) logb (x2 - 8x) 
A)  $\log _ { b } \frac { x ^ { 2 } + 8 } { x }$ 
B)  $\log _ { b } \frac { x + 8 } { x }$ 
C)  $\log _ { b } \frac { x - 8 } { x }$ 
D)  $\log _ { b } \frac { x ^ { 2 } + 8 } { 8 }$ 
E) logb (x2 - 8x)

Question 4

Complete the table to determine the balance A for P dollars invested at rate r for t years and compounded n times per year.  $P = \$ 1100 ; r = 2 \% ; t = 10 \text { year }$

Accepted Answer

A) $\begin{array} { | l | l | l | l | l | l | l | } 
\hline n & 1 & 2 & 4 & 12 & 365 & \text { continuous } \
\hline A & \$ 1,340.89 & \$ 1342.21 & \$ 1,342.87 & \$ 1,343.32 & \$ 1,343.54 & \$ 1,343.54 \
\hline
\end{array}$ 
B) $\begin{array} { | l | l | l | l | l | l | l | } 
\hline n & 1 & 2 & 4 & 12 & 365 & \text { continuous } \
\hline A & \$ 1,340.89 & \$ 1,343.54 & \$ 1,342.87 & \$ 1,343.32 & \$ 1,343.32 & \$ 1,343.54 \
\hline
\end{array}$ 
C) $\begin{array} { | l | l | l | l | l | l | l | } 
\hline n & 1 & 2 & 4 & 12 & 365 & \text { continuous } \
\hline A & \$ 1,340.89 & \$ 1342.21 & \$ 1,340.89 & \$ 1,343.32 & \$ 1,343.32 & \$ 1,343.54 \
\hline
\end{array}$ 
D) $\begin{array} { | l | l | l | l | l | l | l | } 
\hline n & 1 & 2 & 4 & 12 & 365 & \text { continuous } \
\hline A & \$ 1342.21 & \$ 1,340.89 & \$ 1,342.87 & \$ 1,343.32 & \$ 1,343.54 & \$ 1,343.54 \
\hline
\end{array}$ 
E) $\begin{array} { | l | l | l | l | l | l | l | } 
\hline n & 1 & 2 & 4 & 12 & 365 & \text { continuous } \
\hline A & \$ 1,340.89 & \$ 1342.21 & \$ 1,342.87 & \$ 1,343.54 & \$ 1,343.32 & \$ 1,343.32 \
\hline
\end{array}$ 
A) $\begin{array} { | l | l | l | l | l | l | l | } 
\hline n & 1 & 2 & 4 & 12 & 365 & \text { continuous } \
\hline A & \$ 1,340.89 & \$ 1342.21 & \$ 1,342.87 & \$ 1,343.32 & \$ 1,343.54 & \$ 1,343.54 \
\hline
\end{array}$ 
B) $\begin{array} { | l | l | l | l | l | l | l | } 
\hline n & 1 & 2 & 4 & 12 & 365 & \text { continuous } \
\hline A & \$ 1,340.89 & \$ 1,343.54 & \$ 1,342.87 & \$ 1,343.32 & \$ 1,343.32 & \$ 1,343.54 \
\hline
\end{array}$ 
C) $\begin{array} { | l | l | l | l | l | l | l | } 
\hline n & 1 & 2 & 4 & 12 & 365 & \text { continuous } \
\hline A & \$ 1,340.89 & \$ 1342.21 & \$ 1,340.89 & \$ 1,343.32 & \$ 1,343.32 & \$ 1,343.54 \
\hline
\end{array}$ 
D) $\begin{array} { | l | l | l | l | l | l | l | } 
\hline n & 1 & 2 & 4 & 12 & 365 & \text { continuous } \
\hline A & \$ 1342.21 & \$ 1,340.89 & \$ 1,342.87 & \$ 1,343.32 & \$ 1,343.54 & \$ 1,343.54 \
\hline
\end{array}$ 
E) $\begin{array} { | l | l | l | l | l | l | l | } 
\hline n & 1 & 2 & 4 & 12 & 365 & \text { continuous } \
\hline A & \$ 1,340.89 & \$ 1342.21 & \$ 1,342.87 & \$ 1,343.54 & \$ 1,343.32 & \$ 1,343.32 \
\hline
\end{array}$

Question 5

Use the One-to-One Property to solve the equation for x.  $\log _ { 3 } ( x - 4 ) = \log _ { 3 } 6$

Accepted Answer

A) 11 
B) 14 
C) 12 
D) 13 
E) 10 
A) 11 
B) 14 
C) 12 
D) 13 
E) 10

Question 6

Condense the expression to the logarithm of a single quantity.  $\ln x - [ \ln ( x + 6 ) + \ln ( x - 6 ) ]$

Accepted Answer

A)  $\ln \frac { ( x - 6 ) } { x ( x + 6 ) }$ 
B)  $\ln \frac { ( x + 6 ) } { x ( x - 6 ) }$ 
C)  $\ln \frac { x ( x - 6 ) } { ( x + 6 ) }$ 
D)  $\ln \frac { x } { ( x - 6 ) ( x + 6 ) }$ 
E)  $\ln \frac { x ( x + 6 ) } { ( x - 6 ) }$ 
A)  $\ln \frac { ( x - 6 ) } { x ( x + 6 ) }$ 
B)  $\ln \frac { ( x + 6 ) } { x ( x - 6 ) }$ 
C)  $\ln \frac { x ( x - 6 ) } { ( x + 6 ) }$ 
D)  $\ln \frac { x } { ( x - 6 ) ( x + 6 ) }$ 
E)  $\ln \frac { x ( x + 6 ) } { ( x - 6 ) }$

Question 7

Evaluate the function at the indicated value of x.Round your result to three decimal places. 
Function
Value $f ( x ) = 4 ^ { x }$ $x = - \pi$

Accepted Answer

A)  $1.513$ 
B)  $0.013$ 
C)  $0.513$ 
D)  $0.121$ 
E)  $2.0129$ 
A)  $1.513$ 
B)  $0.013$ 
C)  $0.513$ 
D)  $0.121$ 
E)  $2.0129$

Question 8

Solve the logarithmic equation algebraically.Approximate the result to three decimal places.  $\ln \sqrt { x - 8 } = 7$

Accepted Answer

A)  $e ^ { 14 } + 8 \approx 1,202,611.284$ 
B)  $e ^ { 14 } + 8 \approx 1,202,614.284$ 
C)  $e ^ { 14 } + 8 \approx 1,202,612.284$ 
D)  $e ^ { 14 } + 8 \approx 1,202,610.284$ 
E)  $e ^ { 14 } + 8 \approx 1,202,613.284$ 
A)  $e ^ { 14 } + 8 \approx 1,202,611.284$ 
B)  $e ^ { 14 } + 8 \approx 1,202,614.284$ 
C)  $e ^ { 14 } + 8 \approx 1,202,612.284$ 
D)  $e ^ { 14 } + 8 \approx 1,202,610.284$ 
E)  $e ^ { 14 } + 8 \approx 1,202,613.284$

Question 9

Use the properties of logarithms to expand the expression as a sum, difference, and/or constant multiple of logarithms.(Assume all variables are positive.) 
Log3 9x

Accepted Answer

A)  $\frac { \log _ { 3 } 9 } { \log _ { 3 } x }$ 
B) log3 9 × log3 x 
C) log3 9 + log3 x 
D) log3 9 - log3 x 
E) None of these 
A)  $\frac { \log _ { 3 } 9 } { \log _ { 3 } x }$ 
B) log3 9 × log3 x 
C) log3 9 + log3 x 
D) log3 9 - log3 x 
E) None of these

Question 10

Select the correct graph for the given function  $y = 4 e ^ { x / 2 }$

Accepted Answer

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

Question 11

Solve the exponential equation algebraically.Approximate the result to three decimal places.   $4 \left( 5 ^ { x - 5 } \right) = 24$

Accepted Answer

A)  $5 + \frac { \ln 6 } { \ln 5 } \approx 7.113$ 
B)  $5 + \frac { \ln 6 } { \ln 5 } \approx 9.113$ 
C)  $5 + \frac { \ln 6 } { \ln 5 } \approx 6.113$ 
D)  $5 + \frac { \ln 6 } { \ln 5 } \approx 8.113$ 
E)  $5 + \frac { \ln 6 } { \ln 5 } \approx 10.113$ 
A)  $5 + \frac { \ln 6 } { \ln 5 } \approx 7.113$ 
B)  $5 + \frac { \ln 6 } { \ln 5 } \approx 9.113$ 
C)  $5 + \frac { \ln 6 } { \ln 5 } \approx 6.113$ 
D)  $5 + \frac { \ln 6 } { \ln 5 } \approx 8.113$ 
E)  $5 + \frac { \ln 6 } { \ln 5 } \approx 10.113$

Question 12

Use the One-to-One Property to solve the following equation for x. $2 ^ { 5 x } = 128$

Accepted Answer

A)  $\frac { 128 } { 5 }$ 
B)  $- \frac { 64 } { 5 }$ 
C)  $\frac { 7 } { 5 }$ 
D)  $\frac { 5 } { 7 }$ 
E) 2 
A)  $\frac { 128 } { 5 }$ 
B)  $- \frac { 64 } { 5 }$ 
C)  $\frac { 7 } { 5 }$ 
D)  $\frac { 5 } { 7 }$ 
E) 2

Question 13

Solve the exponential equation algebraically.Approximate the result to three decimal places.   $e ^ { x } = e ^ { x ^ { 2 } - 12 }$

Accepted Answer

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

Question 14

Evaluate $g ( x ) = \ln x$ at the indicated value of x. $x = e ^ { 7 }$

Accepted Answer

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

Question 15

Put the expressions in the appropriate order: $\frac { \ln 8 } { \ln e } , \frac { \ln 8 } { e } , \ln 8$ .

Accepted Answer

A)  $\ln 8 < \frac { \ln 8 } { e } < \frac { \ln 8 } { \ln e }$ 
B)  $\frac { \ln 8 } { e } < \frac { \ln 8 } { \ln e } = \ln 8$ 
C)   $\ln 8 < \frac { \ln 8 } { e } = \frac { \ln 8 } { \ln e }$ 
D)  $\frac { \ln 8 } { \ln e } < \ln 8 < \frac { \ln 8 } { \ln e }$ 
E) The expressions are equivalent. 
A)  $\ln 8 < \frac { \ln 8 } { e } < \frac { \ln 8 } { \ln e }$ 
B)  $\frac { \ln 8 } { e } < \frac { \ln 8 } { \ln e } = \ln 8$ 
C)   $\ln 8 < \frac { \ln 8 } { e } = \frac { \ln 8 } { \ln e }$ 
D)  $\frac { \ln 8 } { \ln e } < \ln 8 < \frac { \ln 8 } { \ln e }$ 
E) The expressions are equivalent.

Question 16

Solve the exponential equation algebraically.Approximate the result to three decimal places.  $2 \left( 3 ^ { x } \right) = 36$

Accepted Answer

A)  $\frac { \ln 18 } { \ln 3 } \approx 0.380$ 
B)  $\frac { \ln 18 } { \ln 3 } \approx - 0.380$ 
C)  $\frac { \ln 18 } { \ln 3 } \approx - 2.631$ 
D)  $\frac { \ln 3 } { \ln 18 } \approx 2.631$ 
E)  $\frac { \ln 18 } { \ln 3 } \approx 2.631$ 
A)  $\frac { \ln 18 } { \ln 3 } \approx 0.380$ 
B)  $\frac { \ln 18 } { \ln 3 } \approx - 0.380$ 
C)  $\frac { \ln 18 } { \ln 3 } \approx - 2.631$ 
D)  $\frac { \ln 3 } { \ln 18 } \approx 2.631$ 
E)  $\frac { \ln 18 } { \ln 3 } \approx 2.631$

Question 17

Rewrite the logarithm as a ratio of common logarithms.  $\log _ { x } \frac { 2 } { 11 }$

Accepted Answer

A)  $\frac { \log x } { \log \frac { 2 } { 11 } }$ 
B)  $\frac { \log \frac { 2 } { 11 } } { \log x }$ 
C)  $\log \frac { 2 } { 11 } x$ 
D)  $\log \frac { 11 } { 2 x }$ 
E) None of these 
A)  $\frac { \log x } { \log \frac { 2 } { 11 } }$ 
B)  $\frac { \log \frac { 2 } { 11 } } { \log x }$ 
C)  $\log \frac { 2 } { 11 } x$ 
D)  $\log \frac { 11 } { 2 x }$ 
E) None of these

Question 18

Use the properties of logarithms to expand the expression as a sum, difference, and/or constant multiple of logarithms.(Assume all variables are positive.)  $\log \sqrt [ 7 ] { \frac { x ^ { 2 } } { y ^ { 4 } } }$

Accepted Answer

A)  $\frac { 2 } { 7 } \log x - \frac { 4 } { 7 } \log y$ 
B)  $\frac { 1 } { 14 } \log x + \frac { 1 } { 28 } \log y$ 
C)  $\frac { 7 } { 2 } \log x + \frac { 7 } { 4 } \log y$ 
D)  $14 \log x + 28 \log y$ 
E)  $\frac { 2 } { 7 } \log x + \frac { 4 } { 7 } \log y$ 
A)  $\frac { 2 } { 7 } \log x - \frac { 4 } { 7 } \log y$ 
B)  $\frac { 1 } { 14 } \log x + \frac { 1 } { 28 } \log y$ 
C)  $\frac { 7 } { 2 } \log x + \frac { 7 } { 4 } \log y$ 
D)  $14 \log x + 28 \log y$ 
E)  $\frac { 2 } { 7 } \log x + \frac { 4 } { 7 } \log y$

Question 19

Select the graph of the function.  $f ( x ) = e ^ { 4 x }$

Accepted Answer

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

Question 20

Use a graphing utility to construct a table of values for the function.Round your answer to two decimal places.  $f ( x ) = 2 ^ { x - 1 } + 2$

Accepted Answer

A) $\begin{array} { | c | c | c | c | c | c | } 
\hline x & - 2 & - 1 & 0 & 1 & 2 \
\hline f ( x ) & 2.13 & 2.25 & 2.50 & 3.00 & 4.00 \
\hline
\end{array}$ 
B) $\begin{array} { | c | c | c | c | c | c | } 
\hline x & - 2 & - 1 & 0 & 1 & 2 \
\hline f ( x ) & 2.13 & 2.25 & - 2.50 & 3.00 & 4.00 \
\hline
\end{array}$ 
C) $\begin{array} { | c | c | c | c | c | c | } 
\hline x & - 2 & - 1 & 0 & 1 & 2 \
\hline f ( x ) & 2.13 & - 2.25 & 2.50 & 3.00 & 4.00 \
\hline
\end{array}$ 
D) $\begin{array} { | c | c | c | c | c | c | } 
\hline x & - 2 & - 1 & 0 & 1 & 2 \
\hline f ( x ) & 2.13 & 2.25 & 2.50 & - 3.00 & - 4.00 \
\hline
\end{array}$ 
E) $\begin{array} { | c | c | c | c | c | c | } 
\hline x & - 2 & - 1 & 0 & 1 & 2 \
\hline f ( x ) & - 2.13 & 2.25 & 2.50 & 3.00 & 4.00 \
\hline
\end{array}$ 
A) $\begin{array} { | c | c | c | c | c | c | } 
\hline x & - 2 & - 1 & 0 & 1 & 2 \
\hline f ( x ) & 2.13 & 2.25 & 2.50 & 3.00 & 4.00 \
\hline
\end{array}$ 
B) $\begin{array} { | c | c | c | c | c | c | } 
\hline x & - 2 & - 1 & 0 & 1 & 2 \
\hline f ( x ) & 2.13 & 2.25 & - 2.50 & 3.00 & 4.00 \
\hline
\end{array}$ 
C) $\begin{array} { | c | c | c | c | c | c | } 
\hline x & - 2 & - 1 & 0 & 1 & 2 \
\hline f ( x ) & 2.13 & - 2.25 & 2.50 & 3.00 & 4.00 \
\hline
\end{array}$ 
D) $\begin{array} { | c | c | c | c | c | c | } 
\hline x & - 2 & - 1 & 0 & 1 & 2 \
\hline f ( x ) & 2.13 & 2.25 & 2.50 & - 3.00 & - 4.00 \
\hline
\end{array}$ 
E) $\begin{array} { | c | c | c | c | c | c | } 
\hline x & - 2 & - 1 & 0 & 1 & 2 \
\hline f ( x ) & - 2.13 & 2.25 & 2.50 & 3.00 & 4.00 \
\hline
\end{array}$

Identify the value of the function $f ( x ) = \log _ { 10 } x$ at $x = 315$ .Round to 3 decimal places.

Condense the expression $\frac { 1 } { 3 } \left[ \log _ { 6 } x + \log _ { 6 } 7 \right] - \left[ \log _ { 6 } y \right]$ to the logarithm of a single term.

Assume that x is a positive number.Use the properties of logarithms to write the expression Log_b (x + 8) - log_b x as the logarithm of one quantity.

Complete the table to determine the balance A for P dollars invested at rate r for t years and compounded n times per year. $P = \$ 1100 ; r = 2 \% ; t = 10 \text { year }$

Use the One-to-One Property to solve the equation for x. $\log _ { 3 } ( x - 4 ) = \log _ { 3 } 6$

Condense the expression to the logarithm of a single quantity. $\ln x - [ \ln ( x + 6 ) + \ln ( x - 6 ) ]$

Evaluate the function at the indicated value of x.Round your result to three decimal places. Function Value $f ( x ) = 4 ^ { x }$ $x = - \pi$

Solve the logarithmic equation algebraically.Approximate the result to three decimal places. $\ln \sqrt { x - 8 } = 7$

Use the properties of logarithms to expand the expression as a sum, difference, and/or constant multiple of logarithms.(Assume all variables are positive.) Log₃ 9x

Select the correct graph for the given function $y = 4 e ^ { x / 2 }$

Solve the exponential equation algebraically.Approximate the result to three decimal places. $4 \left( 5 ^ { x - 5 } \right) = 24$

Use the One-to-One Property to solve the following equation for x. $2 ^ { 5 x } = 128$

Solve the exponential equation algebraically.Approximate the result to three decimal places. $e ^ { x } = e ^ { x ^ { 2 } - 12 }$

Evaluate $g ( x ) = \ln x$ at the indicated value of x. $x = e ^ { 7 }$

Put the expressions in the appropriate order: $\frac { \ln 8 } { \ln e } , \frac { \ln 8 } { e } , \ln 8$ .

Solve the exponential equation algebraically.Approximate the result to three decimal places. $2 \left( 3 ^ { x } \right) = 36$

Rewrite the logarithm as a ratio of common logarithms. $\log _ { x } \frac { 2 } { 11 }$

Use the properties of logarithms to expand the expression as a sum, difference, and/or constant multiple of logarithms.(Assume all variables are positive.) $\log \sqrt [ 7 ] { \frac { x ^ { 2 } } { y ^ { 4 } } }$

Select the graph of the function. $f ( x ) = e ^ { 4 x }$

Use a graphing utility to construct a table of values for the function.Round your answer to two decimal places. $f ( x ) = 2 ^ { x - 1 } + 2$

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

Identify the value of the function f(x)=log⁡10xf ( x ) = \log _ { 10 } xf(x)=log10​x at x=315x = 315x=315 .Round to 3 decimal places.

Condense the expression 13[log⁡6x+log⁡67]−[log⁡6y]\frac { 1 } { 3 } \left[ \log _ { 6 } x + \log _ { 6 } 7 \right] - \left[ \log _ { 6 } y \right]31​[log6​x+log6​7]−[log6​y] to the logarithm of a single term.

Assume that x is a positive number.Use the properties of logarithms to write the expression Logb (x + 8) - logb x as the logarithm of one quantity.

Complete the table to determine the balance A for P dollars invested at rate r for t years and compounded n times per year. P=$1100;r=2%;t=10 year P = \$ 1100 ; r = 2 \% ; t = 10 \text { year }P=$1100;r=2%;t=10 year

Use the One-to-One Property to solve the equation for x. log⁡3(x−4)=log⁡36\log _ { 3 } ( x - 4 ) = \log _ { 3 } 6log3​(x−4)=log3​6

Condense the expression to the logarithm of a single quantity. ln⁡x−[ln⁡(x+6)+ln⁡(x−6)]\ln x - [ \ln ( x + 6 ) + \ln ( x - 6 ) ]lnx−[ln(x+6)+ln(x−6)]

Evaluate the function at the indicated value of x.Round your result to three decimal places. Function Value f(x)=4xf ( x ) = 4 ^ { x }f(x)=4x x=−πx = - \pix=−π

Solve the logarithmic equation algebraically.Approximate the result to three decimal places. ln⁡x−8=7\ln \sqrt { x - 8 } = 7lnx−8​=7

Use the properties of logarithms to expand the expression as a sum, difference, and/or constant multiple of logarithms.(Assume all variables are positive.) Log3 9x

Select the correct graph for the given function y=4ex/2y = 4 e ^ { x / 2 }y=4ex/2

Solve the exponential equation algebraically.Approximate the result to three decimal places. 4(5x−5)=244 \left( 5 ^ { x - 5 } \right) = 244(5x−5)=24

Use the One-to-One Property to solve the following equation for x. 25x=1282 ^ { 5 x } = 12825x=128

Solve the exponential equation algebraically.Approximate the result to three decimal places. ex=ex2−12e ^ { x } = e ^ { x ^ { 2 } - 12 }ex=ex2−12

Evaluate g(x)=ln⁡xg ( x ) = \ln xg(x)=lnx at the indicated value of x. x=e7x = e ^ { 7 }x=e7

Put the expressions in the appropriate order: ln⁡8ln⁡e,ln⁡8e,ln⁡8\frac { \ln 8 } { \ln e } , \frac { \ln 8 } { e } , \ln 8lneln8​,eln8​,ln8 .

Solve the exponential equation algebraically.Approximate the result to three decimal places. 2(3x)=362 \left( 3 ^ { x } \right) = 362(3x)=36

Rewrite the logarithm as a ratio of common logarithms. log⁡x211\log _ { x } \frac { 2 } { 11 }logx​112​

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⁡x2y47\log \sqrt [ 7 ] { \frac { x ^ { 2 } } { y ^ { 4 } } }log7y4x2​​

Select the graph of the function. f(x)=e4xf ( x ) = e ^ { 4 x }f(x)=e4x

Use a graphing utility to construct a table of values for the function.Round your answer to two decimal places. f(x)=2x−1+2f ( x ) = 2 ^ { x - 1 } + 2f(x)=2x−1+2

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

Identify the value of the function $f ( x ) = \log _ { 10 } x$ at $x = 315$ .Round to 3 decimal places.

Condense the expression $\frac { 1 } { 3 } \left[ \log _ { 6 } x + \log _ { 6 } 7 \right] - \left[ \log _ { 6 } y \right]$ to the logarithm of a single term.

Assume that x is a positive number.Use the properties of logarithms to write the expression Log_b (x + 8) - log_b x as the logarithm of one quantity.

Complete the table to determine the balance A for P dollars invested at rate r for t years and compounded n times per year. $P = \$ 1100 ; r = 2 \% ; t = 10 \text { year }$

Use the One-to-One Property to solve the equation for x. $\log _ { 3 } ( x - 4 ) = \log _ { 3 } 6$

Condense the expression to the logarithm of a single quantity. $\ln x - [ \ln ( x + 6 ) + \ln ( x - 6 ) ]$

Evaluate the function at the indicated value of x.Round your result to three decimal places. Function Value $f ( x ) = 4 ^ { x }$ $x = - \pi$

Solve the logarithmic equation algebraically.Approximate the result to three decimal places. $\ln \sqrt { x - 8 } = 7$

Use the properties of logarithms to expand the expression as a sum, difference, and/or constant multiple of logarithms.(Assume all variables are positive.) Log₃ 9x

Select the correct graph for the given function $y = 4 e ^ { x / 2 }$

Solve the exponential equation algebraically.Approximate the result to three decimal places. $4 \left( 5 ^ { x - 5 } \right) = 24$

Use the One-to-One Property to solve the following equation for x. $2 ^ { 5 x } = 128$

Solve the exponential equation algebraically.Approximate the result to three decimal places. $e ^ { x } = e ^ { x ^ { 2 } - 12 }$

Evaluate $g ( x ) = \ln x$ at the indicated value of x. $x = e ^ { 7 }$

Put the expressions in the appropriate order: $\frac { \ln 8 } { \ln e } , \frac { \ln 8 } { e } , \ln 8$ .

Solve the exponential equation algebraically.Approximate the result to three decimal places. $2 \left( 3 ^ { x } \right) = 36$

Rewrite the logarithm as a ratio of common logarithms. $\log _ { x } \frac { 2 } { 11 }$

Use the properties of logarithms to expand the expression as a sum, difference, and/or constant multiple of logarithms.(Assume all variables are positive.) $\log \sqrt [ 7 ] { \frac { x ^ { 2 } } { y ^ { 4 } } }$

Select the graph of the function. $f ( x ) = e ^ { 4 x }$

Use a graphing utility to construct a table of values for the function.Round your answer to two decimal places. $f ( x ) = 2 ^ { x - 1 } + 2$