Question 1

Evaluate the function at the indicated value of $x = 64$ .  $f ( x ) = \log _ { 8 } x$

Accepted Answer

A) 0 
B)  $- \frac { 1 } { 2 }$ 
C)  $\frac { 1 } { 2 }$ 
D) -2 
E) 2 
A) 0 
B)  $- \frac { 1 } { 2 }$ 
C)  $\frac { 1 } { 2 }$ 
D) -2 
E) 2

Question 2

Solve the exponential equation algebraically.Approximate the result to three decimal places.   $3 e ^ { x } = 15$

Accepted Answer

A)  $\ln 5 \approx - 1.609$ 
B)  $\ln 5 \approx 1.099$ 
C)  $\ln 5 \approx - 1.099$ 
D)  $\ln 5 \approx 1.609$ 
E)  $\ln 5 \approx 2.708$ 
A)  $\ln 5 \approx - 1.609$ 
B)  $\ln 5 \approx 1.099$ 
C)  $\ln 5 \approx - 1.099$ 
D)  $\ln 5 \approx 1.609$ 
E)  $\ln 5 \approx 2.708$

Question 3

$2500 is invested in an account at interest rate r, compounded continuously.Find the time required for the amount to double.(Approximate the result to two decimal places.)  $r = 0.06$

Accepted Answer

A) 13.55 yr 
B) 10.55 yr 
C) 12.55 yr 
D) 9.55 yr 
E) 11.55 yr 
A) 13.55 yr 
B) 10.55 yr 
C) 12.55 yr 
D) 9.55 yr 
E) 11.55 yr

Question 4

Evaluate the logarithm using the change-of-base formula.Round your result to three decimal places.
​
Log15 1,500
​

Accepted Answer

A) 5.701 
B) 3.701 
C) 2.701 
D) 6.701 
E) 4.701 
A) 5.701 
B) 3.701 
C) 2.701 
D) 6.701 
E) 4.701

Question 5

Solve the logarithmic equation algebraically.Approximate the result to three decimal places.  $\ln x = - 5$

Accepted Answer

A)  $e ^ { - 5 } \approx 2.007$ 
B)  $e ^ { - 5 } \approx 1.007$ 
C)  $e ^ { - 5 } \approx 3.007$ 
D)  $e ^ { - 5 } \approx - 1.993$ 
E)  $e ^ { - 5 } \approx 0.007$ 
A)  $e ^ { - 5 } \approx 2.007$ 
B)  $e ^ { - 5 } \approx 1.007$ 
C)  $e ^ { - 5 } \approx 3.007$ 
D)  $e ^ { - 5 } \approx - 1.993$ 
E)  $e ^ { - 5 } \approx 0.007$

Question 6

Evaluate the logarithm log7 126 using the change of base formula.Round to 3 decimal places.

Accepted Answer

A) 4.836 
B) 2.485 
C) 0.402 
D) 9.411 
E) 2.1 
A) 4.836 
B) 2.485 
C) 0.402 
D) 9.411 
E) 2.1

Question 7

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.If a sample of rain has a pH of 3.3, how many times higher is its $\left[ \mathrm { H } ^ { + } \right]$ than pure water's, which has a pH of 7?

Accepted Answer

A)  $5.0 \times 10 ^ { 4 }$ 
B)  $2.0 \times 10 ^ { 4 }$ 
C)  $2.0 \times 10 ^ { 3 }$ 
D)  $5.0 \times 10 ^ { 3 }$ 
E) 7 
A)  $5.0 \times 10 ^ { 4 }$ 
B)  $2.0 \times 10 ^ { 4 }$ 
C)  $2.0 \times 10 ^ { 3 }$ 
D)  $5.0 \times 10 ^ { 3 }$ 
E) 7

Question 8

Select the graph of the function. $f ( x ) = 6 e ^ { x - 2 } + 7$

Accepted Answer

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

Question 9

The population P (in thousands) of Orlando, Florida from 2000 through 2007 can be modeled by $P = 1530.6 e ^ { k t }$ where t represents the year, with $t = 0$ corresponding to 2000.In 2006, the population of Orlando, Florida was about 1,883,000.00.Find the value of k.

Accepted Answer

A) k = 0.03183 
B) k = 0.02863 
C) k = 0.02163 
D) k = 0.03453 
E) k = 0.03063 
A) k = 0.03183 
B) k = 0.02863 
C) k = 0.02163 
D) k = 0.03453 
E) k = 0.03063

Question 10

Find the value of b that would cause the graph of y = bx to look like the graph below.

Accepted Answer

A)  $b = \frac { 1 } { e ^ { 3 } }$ 
B)  $b = e ^ { 3 }$ 
C)  $b = e$ 
D)  $b = \frac { 1 } { e }$ 
E)  $b = e ^ { 2 }$ 
A)  $b = \frac { 1 } { e ^ { 3 } }$ 
B)  $b = e ^ { 3 }$ 
C)  $b = e$ 
D)  $b = \frac { 1 } { e }$ 
E)  $b = e ^ { 2 }$

Question 11

Write the logarithmic equation $\ln 5 = 1.609 \ldots$ in exponential form.

Accepted Answer

A)  $e ^ { 1.609 \cdots } = 5$ 
B)  $10 ^ { 5 } = 1.609 \ldots$ 
C)  $2.303 ^ { 1.609 \ldots } = 5$ 
D)  $2.303 \times 10 ^ { 5 } = 1.609 \ldots$ 
E)  $e ^ { 5 } = 1.609 \ldots$ 
A)  $e ^ { 1.609 \cdots } = 5$ 
B)  $10 ^ { 5 } = 1.609 \ldots$ 
C)  $2.303 ^ { 1.609 \ldots } = 5$ 
D)  $2.303 \times 10 ^ { 5 } = 1.609 \ldots$ 
E)  $e ^ { 5 } = 1.609 \ldots$

Question 12

The populations P (in thousands) of Pittsburgh, Pennsylvania from 2000 through 2007 can be modeled by $P = \frac { 2632 } { 1 + 0.083 e ^ { 0.0500 t } }$ where t represents the year, with $t = 0$ corresponding to 2000.Use the model to find the numbers of cell sites in the year 2009.

Accepted Answer

A) 2,326,853.00 
B) 2,327,853.00 
C) 2,329,853.00 
D) 2,328,853.00 
E) 2,330,853.00 
A) 2,326,853.00 
B) 2,327,853.00 
C) 2,329,853.00 
D) 2,328,853.00 
E) 2,330,853.00

Question 13

Use the One-to-One Property to solve the equation for x.  $\log _ { 7 } ( x + 5 ) = \log _ { 7 } 15$

Accepted Answer

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

Question 14

Rewrite the logarithm as a ratio of natural logarithms. 
Log1/5 x

Accepted Answer

A)  $\ln \frac { x } { 5 }$ 
B)  $\frac { \ln \frac { 1 } { 5 } } { \ln x }$ 
C)  $\frac { \ln x } { \ln \frac { 1 } { 5 } }$ 
D)  $\ln 5 x$ 
E) None of these 
A)  $\ln \frac { x } { 5 }$ 
B)  $\frac { \ln \frac { 1 } { 5 } } { \ln x }$ 
C)  $\frac { \ln x } { \ln \frac { 1 } { 5 } }$ 
D)  $\ln 5 x$ 
E) None of these

Question 15

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

Accepted Answer

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

Question 16

Evaluate the function at the indicated value of $x = 23.92$ .Round your result to three decimal places. $f ( x ) = \ln x$

Accepted Answer

A) 3.175 
B) -2.076 
C) -3.175 
D) 2.076 
E) 23.92 
A) 3.175 
B) -2.076 
C) -3.175 
D) 2.076 
E) 23.92

Question 17

Use a graphing utility to construct a table of values for the function.Round your answer to three decimal places.  $f ( x ) = 6 e ^ { x - 2 } + 7$

Accepted Answer

A) $\begin{array} { | c | c | c | c | c | c | } 
\hline x & - 2 & - 1 & 0 & 1 & 2 \
\hline&-&\
 f ( x ) & 7.110 & 7.299 & 7.812 & 9.207 & 13 \
\hline
\end{array}$ 
B) $\begin{array}{|c|c|c|c|c|c|}
\hline x & -2 & -1 & 0 & 1 & 2 \
\hline f(x) & 7.110 & 7.299 & 7.812 & 9.\overline{2}07 & 1 \overline{3} \
\hline
\end{array}$ 
C) $\begin{array} { | c | c | c | c | c | c | } 
\hline x & - 2 & - 1 & 0 & 1 & 2 \
\hline f ( x ) & 7.110 & 7.299 & 7.\overline{8}12 & 9.207 & 13 \
\hline
\end{array}$ 
D) $\begin{array} { | c | c | c | c | c | c | } 
\hline x & - 2 & - 1 & 0 & 1 & 2 \
\hline & & & & & \
f ( x ) & 7.110 & 7.299 & 7.812 & 9.207 & 13 \
& & & & & \
\hline
\end{array}$ 
E) $\begin{array} { | c | c | c | c | c | c | } 
\hline x & - 2 & - 1 & 0 & 1 & 2 \
\hline & & & & & \
f ( x ) & 7.110 & 7.\overline{2}99 & 7.812 & 9.207 & 13 \
& & & & & \
\hline
\end{array}$ 
A) $\begin{array} { | c | c | c | c | c | c | } 
\hline x & - 2 & - 1 & 0 & 1 & 2 \
\hline&-&\
 f ( x ) & 7.110 & 7.299 & 7.812 & 9.207 & 13 \
\hline
\end{array}$ 
B) $\begin{array}{|c|c|c|c|c|c|}
\hline x & -2 & -1 & 0 & 1 & 2 \
\hline f(x) & 7.110 & 7.299 & 7.812 & 9.\overline{2}07 & 1 \overline{3} \
\hline
\end{array}$ 
C) $\begin{array} { | c | c | c | c | c | c | } 
\hline x & - 2 & - 1 & 0 & 1 & 2 \
\hline f ( x ) & 7.110 & 7.299 & 7.\overline{8}12 & 9.207 & 13 \
\hline
\end{array}$ 
D) $\begin{array} { | c | c | c | c | c | c | } 
\hline x & - 2 & - 1 & 0 & 1 & 2 \
\hline & & & & & \
f ( x ) & 7.110 & 7.299 & 7.812 & 9.207 & 13 \
& & & & & \
\hline
\end{array}$ 
E) $\begin{array} { | c | c | c | c | c | c | } 
\hline x & - 2 & - 1 & 0 & 1 & 2 \
\hline & & & & & \
f ( x ) & 7.110 & 7.\overline{2}99 & 7.812 & 9.207 & 13 \
& & & & & \
\hline
\end{array}$

Question 18

Use a graphing utility to construct a table of values for the function.Round your answer to three decimal places.   $f ( x ) = 3 e ^ { x + 4 }$

Accepted Answer

A) $\begin{array} { | l | l | l | l | l | l | } 
\hline x & - 2 & - 1 & 0 & 1 & 2 \
\hline & & & & & \
f ( x ) & 22.167 & 60.257 & 163.792 & 445.239 & 1,210.286 \
& & & & & \
\hline
\end{array}$ 
B) $\begin{array} { | l | l | l | l | l | l | } 
\hline x & - 2 & - 1 & 0 & 1 & 2 \
\hline & & & & & \
f ( x ) & 22.167 & 60.257 & 163.792 & 445.239 & 1,210.286 \
& & & & & \
\hline
\end{array}$ . 
C) $\begin{array} { | l | l | l | l | l | l | } 
\hline x & - 2 & - 1 & 0 & 1 & 2 \
\hline & & & & & \
f ( x ) & 22.167 & 60.257 & 163.792 & 445.239 & 1,210.286 \
& & & & & \
\hline
\end{array}$.. 
D) $\begin{array} { | l | l | l | l | l | l | } 
\hline x & - 2 & - 1 & 0 & 1 & 2 \
\hline & - & - & & & \
f ( x ) & 22.167 & 60.257 & 163.792 & 445.239 & 1,210.286 \
& & & & & \
\hline
\end{array}$ 
E) $\begin{array} { | l | l | l | l | l | l | } 
\hline x & - 2 & - 1 & 0 & 1 & 2 \
\hline & - & - & & & \
f ( x ) & 22.167 & 60.257 & 163.792 & 445.239 & 1,210.286 \
& & & & & \
\hline
\end{array}$ ... 
A) $\begin{array} { | l | l | l | l | l | l | } 
\hline x & - 2 & - 1 & 0 & 1 & 2 \
\hline & & & & & \
f ( x ) & 22.167 & 60.257 & 163.792 & 445.239 & 1,210.286 \
& & & & & \
\hline
\end{array}$ 
B) $\begin{array} { | l | l | l | l | l | l | } 
\hline x & - 2 & - 1 & 0 & 1 & 2 \
\hline & & & & & \
f ( x ) & 22.167 & 60.257 & 163.792 & 445.239 & 1,210.286 \
& & & & & \
\hline
\end{array}$ . 
C) $\begin{array} { | l | l | l | l | l | l | } 
\hline x & - 2 & - 1 & 0 & 1 & 2 \
\hline & & & & & \
f ( x ) & 22.167 & 60.257 & 163.792 & 445.239 & 1,210.286 \
& & & & & \
\hline
\end{array}$.. 
D) $\begin{array} { | l | l | l | l | l | l | } 
\hline x & - 2 & - 1 & 0 & 1 & 2 \
\hline & - & - & & & \
f ( x ) & 22.167 & 60.257 & 163.792 & 445.239 & 1,210.286 \
& & & & & \
\hline
\end{array}$ 
E) $\begin{array} { | l | l | l | l | l | l | } 
\hline x & - 2 & - 1 & 0 & 1 & 2 \
\hline & - & - & & & \
f ( x ) & 22.167 & 60.257 & 163.792 & 445.239 & 1,210.286 \
& & & & & \
\hline
\end{array}$ ...

Question 19

Write the logarithmic equation $\ln 4 = 1.386 \ldots$ in exponential form.

Accepted Answer

A)  $e ^ { 1.386 \cdots } = 4$ 
B)  $e ^ { 4 } = 1.386 \ldots$ 
C)  $2.303 e ^ { 1.386 \cdots } = 4$ 
D)  $10 ^ { 4 } = 1.386 \ldots$ 
E)  $2.303 \times 10 ^ { 4 } = 1.386 \ldots$ 
A)  $e ^ { 1.386 \cdots } = 4$ 
B)  $e ^ { 4 } = 1.386 \ldots$ 
C)  $2.303 e ^ { 1.386 \cdots } = 4$ 
D)  $10 ^ { 4 } = 1.386 \ldots$ 
E)  $2.303 \times 10 ^ { 4 } = 1.386 \ldots$

Question 20

Assume that x, y, and z are positive numbers.Use the properties of logarithms to write the expression $- 2 \log _ { b } x - 6 \log _ { b } y + \frac { 1 } { 7 } \log _ { b } z$ as the logarithm of one quantity.

Accepted Answer

A)  $\log _ { b } \frac { z ^ { 1 / 7 } } { x ^ { 6 } y ^ { 2 } }$ 
B)  $\log _ { b } \frac { z ^ { 1 / 6 } } { x ^ { 2 } y ^ { 7 } }$ 
C)  $\log _ { b } \frac { z ^ { 1 / 2 } } { x ^ { 7 } y ^ { 6 } }$ 
D)  $\log _ { b } \frac { x ^ { 1 / 7 } } { y ^ { 2 } z ^ { 6 } }$ 
E)  $\log _ { b } \frac { z ^ { 1 / 7 } } { x ^ { 2 } y ^ { 6 } }$ 
A)  $\log _ { b } \frac { z ^ { 1 / 7 } } { x ^ { 6 } y ^ { 2 } }$ 
B)  $\log _ { b } \frac { z ^ { 1 / 6 } } { x ^ { 2 } y ^ { 7 } }$ 
C)  $\log _ { b } \frac { z ^ { 1 / 2 } } { x ^ { 7 } y ^ { 6 } }$ 
D)  $\log _ { b } \frac { x ^ { 1 / 7 } } { y ^ { 2 } z ^ { 6 } }$ 
E)  $\log _ { b } \frac { z ^ { 1 / 7 } } { x ^ { 2 } y ^ { 6 } }$

Evaluate the function at the indicated value of $x = 64$ . $f ( x ) = \log _ { 8 } x$

Solve the exponential equation algebraically.Approximate the result to three decimal places. $3 e ^ { x } = 15$

$2500 is invested in an account at interest rate r, compounded continuously.Find the time required for the amount to double.(Approximate the result to two decimal places.) $r = 0.06$

Evaluate the logarithm using the change-of-base formula.Round your result to three decimal places. Log₁₅ 1,500

Solve the logarithmic equation algebraically.Approximate the result to three decimal places. $\ln x = - 5$

Evaluate the logarithm log₇ 126 using the change of base formula.Round to 3 decimal places.

Select the graph of the function. $f ( x ) = 6 e ^ { x - 2 } + 7$

The population P (in thousands) of Orlando, Florida from 2000 through 2007 can be modeled by $P = 1530.6 e ^ { k t }$ where t represents the year, with $t = 0$ corresponding to 2000.In 2006, the population of Orlando, Florida was about 1,883,000.00.Find the value of k.

Find the value of b that would cause the graph of y = b^x to look like the graph below.

Write the logarithmic equation $\ln 5 = 1.609 \ldots$ in exponential form.

The populations P (in thousands) of Pittsburgh, Pennsylvania from 2000 through 2007 can be modeled by $P = \frac { 2632 } { 1 + 0.083 e ^ { 0.0500 t } }$ where t represents the year, with $t = 0$ corresponding to 2000.Use the model to find the numbers of cell sites in the year 2009.

Use the One-to-One Property to solve the equation for x. $\log _ { 7 } ( x + 5 ) = \log _ { 7 } 15$

Rewrite the logarithm as a ratio of natural logarithms. Log_1/5 x

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

Evaluate the function at the indicated value of $x = 23.92$ .Round your result to three decimal places. $f ( x ) = \ln x$

Use a graphing utility to construct a table of values for the function.Round your answer to three decimal places. $f ( x ) = 6 e ^ { x - 2 } + 7$

Use a graphing utility to construct a table of values for the function.Round your answer to three decimal places. $f ( x ) = 3 e ^ { x + 4 }$

Write the logarithmic equation $\ln 4 = 1.386 \ldots$ in exponential form.

Assume that x, y, and z are positive numbers.Use the properties of logarithms to write the expression $- 2 \log _ { b } x - 6 \log _ { b } y + \frac { 1 } { 7 } \log _ { b } z$ as the logarithm of one quantity.

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

Evaluate the function at the indicated value of x=64x = 64x=64 . f(x)=log⁡8xf ( x ) = \log _ { 8 } xf(x)=log8​x

Solve the exponential equation algebraically.Approximate the result to three decimal places. 3ex=153 e ^ { x } = 153ex=15

$2500 is invested in an account at interest rate r, compounded continuously.Find the time required for the amount to double.(Approximate the result to two decimal places.) r=0.06r = 0.06r=0.06

Evaluate the logarithm using the change-of-base formula.Round your result to three decimal places. ​ Log15 1,500 ​

Solve the logarithmic equation algebraically.Approximate the result to three decimal places. ln⁡x=−5\ln x = - 5lnx=−5

Evaluate the logarithm log7 126 using the change of base formula.Round to 3 decimal places.

Select the graph of the function. f(x)=6ex−2+7f ( x ) = 6 e ^ { x - 2 } + 7f(x)=6ex−2+7

The population P (in thousands) of Orlando, Florida from 2000 through 2007 can be modeled by P=1530.6ektP = 1530.6 e ^ { k t }P=1530.6ekt where t represents the year, with t=0t = 0t=0 corresponding to 2000.In 2006, the population of Orlando, Florida was about 1,883,000.00.Find the value of k.

Find the value of b that would cause the graph of y = bx to look like the graph below.

Write the logarithmic equation ln⁡5=1.609…\ln 5 = 1.609 \ldotsln5=1.609… in exponential form.

Use the One-to-One Property to solve the equation for x. log⁡7(x+5)=log⁡715\log _ { 7 } ( x + 5 ) = \log _ { 7 } 15log7​(x+5)=log7​15

Rewrite the logarithm as a ratio of natural logarithms. Log1/5 x

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

Evaluate the function at the indicated value of x=23.92x = 23.92x=23.92 .Round your result to three decimal places. f(x)=ln⁡xf ( x ) = \ln xf(x)=lnx

Use a graphing utility to construct a table of values for the function.Round your answer to three decimal places. f(x)=6ex−2+7f ( x ) = 6 e ^ { x - 2 } + 7f(x)=6ex−2+7

Use a graphing utility to construct a table of values for the function.Round your answer to three decimal places. f(x)=3ex+4f ( x ) = 3 e ^ { x + 4 }f(x)=3ex+4

Write the logarithmic equation ln⁡4=1.386…\ln 4 = 1.386 \ldotsln4=1.386… in exponential form.

Assume that x, y, and z are positive numbers.Use the properties of logarithms to write the expression −2log⁡bx−6log⁡by+17log⁡bz- 2 \log _ { b } x - 6 \log _ { b } y + \frac { 1 } { 7 } \log _ { b } z−2logb​x−6logb​y+71​logb​z as the logarithm of one quantity.

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 the function at the indicated value of $x = 64$ . $f ( x ) = \log _ { 8 } x$

Solve the exponential equation algebraically.Approximate the result to three decimal places. $3 e ^ { x } = 15$

$2500 is invested in an account at interest rate r, compounded continuously.Find the time required for the amount to double.(Approximate the result to two decimal places.) $r = 0.06$

Evaluate the logarithm using the change-of-base formula.Round your result to three decimal places. Log₁₅ 1,500

Solve the logarithmic equation algebraically.Approximate the result to three decimal places. $\ln x = - 5$

Evaluate the logarithm log₇ 126 using the change of base formula.Round to 3 decimal places.

Select the graph of the function. $f ( x ) = 6 e ^ { x - 2 } + 7$

The population P (in thousands) of Orlando, Florida from 2000 through 2007 can be modeled by $P = 1530.6 e ^ { k t }$ where t represents the year, with $t = 0$ corresponding to 2000.In 2006, the population of Orlando, Florida was about 1,883,000.00.Find the value of k.

Find the value of b that would cause the graph of y = b^x to look like the graph below.

Write the logarithmic equation $\ln 5 = 1.609 \ldots$ in exponential form.

Use the One-to-One Property to solve the equation for x. $\log _ { 7 } ( x + 5 ) = \log _ { 7 } 15$

Rewrite the logarithm as a ratio of natural logarithms. Log_1/5 x

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

Evaluate the function at the indicated value of $x = 23.92$ .Round your result to three decimal places. $f ( x ) = \ln x$

Use a graphing utility to construct a table of values for the function.Round your answer to three decimal places. $f ( x ) = 6 e ^ { x - 2 } + 7$

Use a graphing utility to construct a table of values for the function.Round your answer to three decimal places. $f ( x ) = 3 e ^ { x + 4 }$

Write the logarithmic equation $\ln 4 = 1.386 \ldots$ in exponential form.

Assume that x, y, and z are positive numbers.Use the properties of logarithms to write the expression $- 2 \log _ { b } x - 6 \log _ { b } y + \frac { 1 } { 7 } \log _ { b } z$ as the logarithm of one quantity.