Question 1

Evaluate without the use of a calculator. $\log _ { t } t ^ { 19 }$

Accepted Answer

A)  $\frac { 1 } { 19 }$ 
B)  19 
C)  $- 19$ 
D)  1 
A)  $\frac { 1 } { 19 }$ 
B)  19 
C)  $- 19$ 
D)  1

Question 2

If both $f$ and $g$ are one-to-one functions, and $( f \circ g ) ( x ) = x ^ { 3 }$, then which of the following is/are true?

Accepted Answer

A)  $( g \circ f ) ( x ) = x ^ { - 3 }$ 
B)  $g$ is the inverse function of $f$ 
C)  $f$ is the inverse function of $g$ 
D)  None of the above is true. 
A)  $( g \circ f ) ( x ) = x ^ { - 3 }$ 
B)  $g$ is the inverse function of $f$ 
C)  $f$ is the inverse function of $g$ 
D)  None of the above is true.

Question 3

Write the expression as a single logarithm. Assume all variables represent positive real numbers. $12 \log x + 15 \log y$

Accepted Answer

A)  $\log \left( x ^ { 12 } + y ^ { 15 } \right)$ 
B)  $\log ( 12 x + 15 y )$ 
C)  $\log \left( x ^ { 12 } y ^ { 15 } \right)$ 
D)  $\log \frac { x ^ { 12 } } { y ^ { 15 } }$ 
A)  $\log \left( x ^ { 12 } + y ^ { 15 } \right)$ 
B)  $\log ( 12 x + 15 y )$ 
C)  $\log \left( x ^ { 12 } y ^ { 15 } \right)$ 
D)  $\log \frac { x ^ { 12 } } { y ^ { 15 } }$

Question 4

Use a calculator to approximate the logarithm. Round to 3 decimal places. $\log 0.000005$

Accepted Answer

A)  $- 5.301$ 
B)  $- 12.206$ 
C)  $2.614$ 
D)  $- 8.143$ 
A)  $- 5.301$ 
B)  $- 12.206$ 
C)  $2.614$ 
D)  $- 8.143$

Question 5

Use the change-of-base formula to approximate the logarithm to four decimal places. $$\log _ { 7 } 29$$

Accepted Answer

A)  0.5779 
B)  1.7304 
C)  1.4624 
D)  3.3673 
A)  0.5779 
B)  1.7304 
C)  1.4624 
D)  3.3673

Question 6

A professor discovers that the GPA of a student at her university can be estimated reasonably well using the formula $G = \log \left( \frac { h } { d + 1 } \right) ^ { 1.9 }$ where h is the total number of hours spent studying outside of class in a semester, d is the number of classes missed during the semester, and G is the student's GPA for the semester. Expand this formula using properties of logs, and use your answer to find the expected semester GPA of a student that studies for 300 hours and misses 2 classes.

Accepted Answer

The answer of A professor discovers that the GPA of...

Question 7

Solve the exponential equation by taking a logarithm of both sides. $$7 ^ { a } = 15$$

Accepted Answer

A)  $\left\{ \ln \frac { 15 } { 7 } \right\}$ 
B)  $\left\{ \ln \frac { 7 } { 15 } \right\}$ 
C)  $\left\{ \frac { \ln 15 } { \ln 7 } \right\}$ 
D)  $\left\{ \frac { \ln 7 } { \ln 15 } \right\}$ 
A)  $\left\{ \ln \frac { 15 } { 7 } \right\}$ 
B)  $\left\{ \ln \frac { 7 } { 15 } \right\}$ 
C)  $\left\{ \frac { \ln 15 } { \ln 7 } \right\}$ 
D)  $\left\{ \frac { \ln 7 } { \ln 15 } \right\}$

Question 8

Graph the equation by completing the table and plotting points. Round to two decimal places when necessary. $g(x)=\ln (x-3)$
$\begin{array}{l|l}
x & y \
\hline 3.5 & \
\hline 4 & \
\hline 6 & \
\hline 8 &
\end{array}$

Accepted Answer

\[\begin{array} { l | l } 
x &

Question 9

In many cases, the population of a town can be predicted using the same formula that is used to compute the balance of an account with interest compounded continuously. If a town has 14,850 citizens now, and grows at 4.5% per year, predict the population in 10 years to the nearest whole number. [Hint: in the formula for continuously-compounded interest, substitute the current population for the principal. The result (amount) will correspond to the new population.]

Accepted Answer

The answer of In many cases, the population of a...

Question 10

Solve the logarithmic equation. $\log ( x + 45 ) = - 9.4$

Accepted Answer

A)  $\left\{ 10 ^ { 45 } - 9.4 \right\}$ 
B)  $\left\{ e ^ { - 9.4 } - 45 \right\}$ 
C)  $\left\{ 10 ^ { - 9.4 } - 45 \right\}$ 
D)  $\left\{ e ^ { 45 } - 9.4 \right\}$ 
A)  $\left\{ 10 ^ { 45 } - 9.4 \right\}$ 
B)  $\left\{ e ^ { - 9.4 } - 45 \right\}$ 
C)  $\left\{ 10 ^ { - 9.4 } - 45 \right\}$ 
D)  $\left\{ e ^ { 45 } - 9.4 \right\}$

Question 11

Graph the function $f ( x ) = 2 ^ { x + 2 }$ . Plot at least three points.

Accepted Answer

The answer of Graph the function \(f ( x )...

Question 12

Graph the equation by completing the table and plotting points. Round to two decimal places when necessary. $f(x)=2 \ln x$
$\begin{array}{l|l}
x & y \
\hline 0.5 & \
\hline 1 & \
\hline 4 & \
\hline 8 &
\end{array}$

Accepted Answer

None

Question 13

Determine if the function is one-to-one by using the horizontal line test.

Accepted Answer

A)  Not one-to-one 
B)  One-to-one 
A)  Not one-to-one 
B)  One-to-one

Question 14

If $m ( x ) = x - 7$ and $n ( x ) = \frac { 1 } { x + 7 }$ find the function value, if possible. $( m \cdot n ) ( 7 )$

Accepted Answer

A)  0 
B)  $\frac { 1 } { 14 }$ 
C)  1 
D)  Undefined 
A)  0 
B)  $\frac { 1 } { 14 }$ 
C)  1 
D)  Undefined

Question 15

Solve the logarithmic equation. $$\log _ { 8 } ( 10 x ) = 2$$

Accepted Answer

A)  $\left\{ \frac { 8 } { 5 } \right\}$ 
B)  $\left\{ \frac { 32 } { 5 } \right\}$ 
C)  $\{ 20 \}$ 
D)  $\{ - 8 \}$ 
A)  $\left\{ \frac { 8 } { 5 } \right\}$ 
B)  $\left\{ \frac { 32 } { 5 } \right\}$ 
C)  $\{ 20 \}$ 
D)  $\{ - 8 \}$

Question 16

Solve the logarithmic equation. $$14 - 13 \log _ { 3 } ( x - 5 ) = 1$$

Accepted Answer

A) {  } 
B)  $\left\{ \frac { 11 } { 3 } \right\}$ 
C)  $\{ 8 \}$ 
D)  $\{ - 5 \}$ 
A) {  } 
B)  $\left\{ \frac { 11 } { 3 } \right\}$ 
C)  $\{ 8 \}$ 
D)  $\{ - 5 \}$

Question 17

Evaluate without the use of a calculator. $$\log _ { t } \frac { 1 } { t }$$

Accepted Answer

The answer of Evaluate without the use of a calculator....

Question 18

A particular type of radioactive medical waste is shipped to a "cooling-down" facility in sealed plastic barrels where it is housed until the radiation intensity falls below a fixed threshold. Upon arrival, a barrel contains 6 pounds of the radioactive material and must be stored until the radioactive component has decayed to 1 pound or less, after which time the barrel may be shipped out for final disposal. If the amount of radioactive waste in a barrel is given by the formula $A = 6 e ^ { - 0.02 t }$ where t is the number of days after arrival, how long must a barrel be stored before it can be shipped for final disposal? Round to the nearest tenth of a day.

Accepted Answer

The answer of A particular type of radioactive medical waste...

Question 19

Find the value of $\log _ { b } \left( \frac { 49 } { 4 } \right)$, given that $\log _ { b } 4 = 1.266$ and $\log _ { b } 7 = 1.777$.

Accepted Answer

A)  $2.288$ 
B)  $1.892$ 
C)  $4.820$ 
D)  $0.511$ 
A)  $2.288$ 
B)  $1.892$ 
C)  $4.820$ 
D)  $0.511$

Question 20

Write an equation of the inverse for the one-to-one function $$h ( x ) = \sqrt [ 5 ] { x } - 6$$

Accepted Answer

The answer of Write an equation of the inverse for...

Evaluate without the use of a calculator. $\log _ { t } t ^ { 19 }$

If both $f$ and $g$ are one-to-one functions, and $( f \circ g ) ( x ) = x ^ { 3 }$ , then which of the following is/are true?

Write the expression as a single logarithm. Assume all variables represent positive real numbers. $12 \log x + 15 \log y$

Use a calculator to approximate the logarithm. Round to 3 decimal places. $\log 0.000005$

Use the change-of-base formula to approximate the logarithm to four decimal places. $\log _ { 7 } 29$

Solve the exponential equation by taking a logarithm of both sides. $7 ^ { a } = 15$

Graph the equation by completing the table and plotting points. Round to two decimal places when necessary. $g(x)=\ln (x-3)$ x y 3.5 4 6 8

Solve the logarithmic equation. $\log ( x + 45 ) = - 9.4$

Graph the function $f ( x ) = 2 ^ { x + 2 }$ . Plot at least three points.

Graph the equation by completing the table and plotting points. Round to two decimal places when necessary. $f(x)=2 \ln x$ x y 0.5 1 4 8

Determine if the function is one-to-one by using the horizontal line test.

If $m ( x ) = x - 7$ and $n ( x ) = \frac { 1 } { x + 7 }$ find the function value, if possible. $( m \cdot n ) ( 7 )$

Solve the logarithmic equation. $\log _ { 8 } ( 10 x ) = 2$

Solve the logarithmic equation. $14 - 13 \log _ { 3 } ( x - 5 ) = 1$

Evaluate without the use of a calculator. $\log _ { t } \frac { 1 } { t }$

Find the value of $\log _ { b } \left( \frac { 49 } { 4 } \right)$ , given that $\log _ { b } 4 = 1.266$ and $\log _ { b } 7 = 1.777$ .

Write an equation of the inverse for the one-to-one function $h ( x ) = \sqrt [ 5 ] { x } - 6$

Linear Equations and Inequalities in One Variable

Linear Equations in Two Variables and Functions

Systems of Linear Equations and Inequalities

Polynomials

Rational Expressions and Rational Equations

Radicals and Complex Numbers

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Exam 8: Exponential and Logarithmic Functions and Applications

Evaluate without the use of a calculator. log⁡tt19\log _ { t } t ^ { 19 }logt​t19

If both fff and ggg are one-to-one functions, and (f∘g)(x)=x3( f \circ g ) ( x ) = x ^ { 3 }(f∘g)(x)=x3 , then which of the following is/are true?

Write the expression as a single logarithm. Assume all variables represent positive real numbers. 12log⁡x+15log⁡y12 \log x + 15 \log y12logx+15logy

Use a calculator to approximate the logarithm. Round to 3 decimal places. log⁡0.000005\log 0.000005log0.000005

Use the change-of-base formula to approximate the logarithm to four decimal places. log⁡729\log _ { 7 } 29log7​29

Solve the exponential equation by taking a logarithm of both sides. 7a=157 ^ { a } = 157a=15

Graph the equation by completing the table and plotting points. Round to two decimal places when necessary. g(x)=ln⁡(x−3)g(x)=\ln (x-3)g(x)=ln(x−3) x y 3.5 4 6 8

Solve the logarithmic equation. log⁡(x+45)=−9.4\log ( x + 45 ) = - 9.4log(x+45)=−9.4

Graph the function f(x)=2x+2f ( x ) = 2 ^ { x + 2 }f(x)=2x+2 . Plot at least three points.

Graph the equation by completing the table and plotting points. Round to two decimal places when necessary. f(x)=2ln⁡xf(x)=2 \ln xf(x)=2lnx x y 0.5 1 4 8

Determine if the function is one-to-one by using the horizontal line test.

If m(x)=x−7m ( x ) = x - 7m(x)=x−7 and n(x)=1x+7n ( x ) = \frac { 1 } { x + 7 }n(x)=x+71​ find the function value, if possible. (m⋅n)(7)( m \cdot n ) ( 7 )(m⋅n)(7)

Solve the logarithmic equation. log⁡8(10x)=2\log _ { 8 } ( 10 x ) = 2log8​(10x)=2

Solve the logarithmic equation. 14−13log⁡3(x−5)=114 - 13 \log _ { 3 } ( x - 5 ) = 114−13log3​(x−5)=1

Evaluate without the use of a calculator. log⁡t1t\log _ { t } \frac { 1 } { t }logt​t1​

Find the value of log⁡b(494)\log _ { b } \left( \frac { 49 } { 4 } \right)logb​(449​) , given that log⁡b4=1.266\log _ { b } 4 = 1.266logb​4=1.266 and log⁡b7=1.777\log _ { b } 7 = 1.777logb​7=1.777 .

Write an equation of the inverse for the one-to-one function h(x)=x5−6h ( x ) = \sqrt [ 5 ] { x } - 6h(x)=5x​−6

Linear Equations and Inequalities in One Variable

Linear Equations in Two Variables and Functions

Systems of Linear Equations and Inequalities

Polynomials

Rational Expressions and Rational Equations

Radicals and Complex Numbers

Quadratic Equations, Functions and Inequalities

Conic Sections

Binomial Expansions, Sequences, and Series

Online: Transformations, Piecewise-Defined Functions, and Probability

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Evaluate without the use of a calculator. $\log _ { t } t ^ { 19 }$

If both $f$ and $g$ are one-to-one functions, and $( f \circ g ) ( x ) = x ^ { 3 }$ , then which of the following is/are true?

Write the expression as a single logarithm. Assume all variables represent positive real numbers. $12 \log x + 15 \log y$

Use a calculator to approximate the logarithm. Round to 3 decimal places. $\log 0.000005$

Use the change-of-base formula to approximate the logarithm to four decimal places. $\log _ { 7 } 29$

Solve the exponential equation by taking a logarithm of both sides. $7 ^ { a } = 15$

Graph the equation by completing the table and plotting points. Round to two decimal places when necessary. $g(x)=\ln (x-3)$ x y 3.5 4 6 8

Solve the logarithmic equation. $\log ( x + 45 ) = - 9.4$

Graph the function $f ( x ) = 2 ^ { x + 2 }$ . Plot at least three points.

Graph the equation by completing the table and plotting points. Round to two decimal places when necessary. $f(x)=2 \ln x$ x y 0.5 1 4 8

If $m ( x ) = x - 7$ and $n ( x ) = \frac { 1 } { x + 7 }$ find the function value, if possible. $( m \cdot n ) ( 7 )$

Solve the logarithmic equation. $\log _ { 8 } ( 10 x ) = 2$

Solve the logarithmic equation. $14 - 13 \log _ { 3 } ( x - 5 ) = 1$

Evaluate without the use of a calculator. $\log _ { t } \frac { 1 } { t }$

Find the value of $\log _ { b } \left( \frac { 49 } { 4 } \right)$ , given that $\log _ { b } 4 = 1.266$ and $\log _ { b } 7 = 1.777$ .

Write an equation of the inverse for the one-to-one function $h ( x ) = \sqrt [ 5 ] { x } - 6$