Question 1

Let $n=\log p$ and $m=\log q$. What is $\log \frac{p^{6}}{q^{7}}$ ?

Accepted Answer

A)  $\frac{n^{6}}{m^{7}}$ 
B)  $\left(\frac{n}{m}\right)^{-1}$ 
C)  $(n-m)^{-1}$ 
D)  $6 n-7 m$ 
A)  $\frac{n^{6}}{m^{7}}$ 
B)  $\left(\frac{n}{m}\right)^{-1}$ 
C)  $(n-m)^{-1}$ 
D)  $6 n-7 m$ D

Question 2

Let $n=\log p$. What is $\log \sqrt[6]{p}$ ?

Accepted Answer

A)  $\sqrt[6]{n}$ 
B)  $\frac{1}{6} n$ 
C)  $n^{6}$ 
D)  $\frac{6}{n}$ 
A)  $\sqrt[6]{n}$ 
B)  $\frac{1}{6} n$ 
C)  $n^{6}$ 
D)  $\frac{6}{n}$ B

Question 3

Does $\ln \left(x^{4} e^{-\ln \sqrt{x}}\right)=\frac{7}{2} \ln x$ ?

Accepted Answer

A) True 
 B)False  True

Question 4

If $Q=\frac{1}{7} e^{0.062 t}$ is converted to the form $Q=a b^{t}$, then $b=\ldots$. Round to 3 decimal places.

Accepted Answer

The answer of If $Q=\frac{1}{7} e^{0.062 t}$ is converted to...

Question 5

Evaluate $e^{\ln \left(5^{2}\right)}$ without a calculator.

Accepted Answer

The answer of Evaluate $e^{\ln \left(5^{2}\right)}$ without a calculator....

Question 6

Find the domain of the function $f(x)=\sqrt{9 \ln (x-7)}-6$.

Accepted Answer

The answer of Find the domain of the function \(f(x)=\sqrt{9...

Question 7

A town with an initial population of 12,000 people doubles every 41 years. Determine the town's population after 12 years.

Accepted Answer

The answer of A town with an initial population of...

Question 8

Consider the function $f(x)=-55^{-x}+2$.
A) Graph the function.
B) State the domain.
C) State all asymptotes.

Accepted Answer

Part A:
 @#IMG-DLM& 
Part B: A

Question 9

Find a possible formula for the following graph using either logarithms or exponentials.

Accepted Answer

The answer of Find a possible formula for the following...

Question 10

The following table gives $z$ as a linear function of $x$.
 
If $z=\ln y$, which of the following is a formula for $y$ in terms of $x$ ?

Accepted Answer

A)  $y=\ln (-2+-5 x)$ 
B)  $y=e^{-2-5 x}$ 
C)  $y=-2 \ln (-5 x)$ 
D)  $y=-2 e^{-5 x}$ 
A)  $y=\ln (-2+-5 x)$ 
B)  $y=e^{-2-5 x}$ 
C)  $y=-2 \ln (-5 x)$ 
D)  $y=-2 e^{-5 x}$

Question 11

What annual interest rate, compounded monthly, is equivalent to an annual interest rate of 5.4% compounded continuously? Round your answer to the nearest thousandth of a percent, if necessary.

Accepted Answer

The answer of What annual interest rate, compounded monthly, is...

Question 12

Let $y=20 e^{-0.07 t}$, with $t$ measured in years. What is the continuous percent decay rate per year?

Accepted Answer

The answer of Let $y=20 e^{-0.07 t}$, with $t$ measured...

Question 13

Let $f(x)=\log (4 x), g(x)=\log (2 x)$, and $h(x)=\frac{f(x)-g(x)}{f(x)+g(x)}$, with $x>0$. Which of the following is a simplified formula for $h(x)$ ?

Accepted Answer

A)  $\frac{\log (2 x)}{\log (6 x)}$ 
B)  $\log \left(\frac{1}{3}\right)$ 
C)  $ 2 \log (4 x)+2 \log (2 x)$ 
D)  $\frac{\log (2)}{\log \left(8 x^{2}\right)}$ 
A)  $\frac{\log (2 x)}{\log (6 x)}$ 
B)  $\log \left(\frac{1}{3}\right)$ 
C)  $ 2 \log (4 x)+2 \log (2 x)$ 
D)  $\frac{\log (2)}{\log \left(8 x^{2}\right)}$

Question 14

Evaluate $\log (\sqrt[5]{10})$ without a calculator. Leave fractions in the form "A\B" (do not convert to decimals).

Accepted Answer

The answer of Evaluate $\log (\sqrt[5]{10})$ without a calculator. Leave...

Question 15

How many times more powerful is an earthquake measuring 5.6 on the Richter scale than an earthquake measuring 4.5 on the Richter scale? Round your answer to two decimal places.

Accepted Answer

The earthquake measuring 5.6 o

Question 16

Evaluate $\log \left(10^{19}\right)$

Accepted Answer

The answer of Evaluate $\log \left(10^{19}\right)$...

Question 17

Let $f(x)=\log (x-1)-1$.
A) $\operatorname{Graph} f$.
B) What are the asymptotes?
C) What are the intercepts if they exist?

Accepted Answer

Part A:
 @#IMG-DLM& 
Part B: H

Question 18

Let $n=\log p$ and $m=\log q$. What is $\log \left(p^{5} q^{4}\right)$ ?

Accepted Answer

A)  $5 n+4 m$ 
B)  $20 \mathrm{~nm}$ 
C)  $n^{5}+m^{4}$ 
D)  $\mathrm{nm}^{9}$ 
A)  $5 n+4 m$ 
B)  $20 \mathrm{~nm}$ 
C)  $n^{5}+m^{4}$ 
D)  $\mathrm{nm}^{9}$

Question 19

Rewriting $10^{3}=1000$ using logs gives

Accepted Answer

A)  $ \log (1000)=-3$ 
B)  $\log (3)=-1000$ 
C)  $ \log (1000)=3$ 
D)  $\log (3)=1000$ 
A)  $ \log (1000)=-3$ 
B)  $\log (3)=-1000$ 
C)  $ \log (1000)=3$ 
D)  $\log (3)=1000$

Question 20

Find $\lim _{x \rightarrow 6^{+}} \ln (x-6)$.

Accepted Answer

The answer of Find $\lim _{x \rightarrow 6^{+}} \ln (x-6)$....

Let $n=\log p$ and $m=\log q$ . What is $\log \frac{p^{6}}{q^{7}}$ ?

Let $n=\log p$ . What is $\log \sqrt[6]{p}$ ?

Does $\ln \left(x^{4} e^{-\ln \sqrt{x}}\right)=\frac{7}{2} \ln x$ ?

If $Q=\frac{1}{7} e^{0.062 t}$ is converted to the form $Q=a b^{t}$ , then $b=\ldots$ . Round to 3 decimal places.

Evaluate $e^{\ln \left(5^{2}\right)}$ without a calculator.

Find the domain of the function $f(x)=\sqrt{9 \ln (x-7)}-6$ .

A town with an initial population of 12,000 people doubles every 41 years. Determine the town's population after 12 years.

Consider the function $f(x)=-55^{-x}+2$ . A) Graph the function. B) State the domain. C) State all asymptotes.

Find a possible formula for the following graph using either logarithms or exponentials.

The following table gives $z$ as a linear function of $x$ . $The following table gives z as a linear function of x . If z=\ln y , which of the following is a formula for y in terms of x ?$ If $z=\ln y$ , which of the following is a formula for $y$ in terms of $x$ ?

What annual interest rate, compounded monthly, is equivalent to an annual interest rate of 5.4% compounded continuously? Round your answer to the nearest thousandth of a percent, if necessary.

Let $y=20 e^{-0.07 t}$ , with $t$ measured in years. What is the continuous percent decay rate per year?

Let $f(x)=\log (4 x), g(x)=\log (2 x)$ , and $h(x)=\frac{f(x)-g(x)}{f(x)+g(x)}$ , with $x>0$ . Which of the following is a simplified formula for $h(x)$ ?

Evaluate $\log (\sqrt[5]{10})$ without a calculator. Leave fractions in the form "A\B" (do not convert to decimals).

How many times more powerful is an earthquake measuring 5.6 on the Richter scale than an earthquake measuring 4.5 on the Richter scale? Round your answer to two decimal places.

Evaluate $\log \left(10^{19}\right)$

Let $f(x)=\log (x-1)-1$ . A) $\operatorname{Graph} f$ . B) What are the asymptotes? C) What are the intercepts if they exist?

Let $n=\log p$ and $m=\log q$ . What is $\log \left(p^{5} q^{4}\right)$ ?

Rewriting $10^{3}=1000$ using logs gives

Find $\lim _{x \rightarrow 6^{+}} \ln (x-6)$ .

Linear Functions and Change

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Exam 5: Logarithmic Functions

Let n=log⁡pn=\log pn=logp and m=log⁡qm=\log qm=logq . What is log⁡p6q7\log \frac{p^{6}}{q^{7}}logq7p6​ ?

Let n=log⁡pn=\log pn=logp . What is log⁡p6\log \sqrt[6]{p}log6p​ ?

Does ln⁡(x4e−ln⁡x)=72ln⁡x\ln \left(x^{4} e^{-\ln \sqrt{x}}\right)=\frac{7}{2} \ln xln(x4e−lnx​)=27​lnx ?

If Q=17e0.062tQ=\frac{1}{7} e^{0.062 t}Q=71​e0.062t is converted to the form Q=abtQ=a b^{t}Q=abt , then b=…b=\ldotsb=… . Round to 3 decimal places.

Evaluate eln⁡(52)e^{\ln \left(5^{2}\right)}eln(52) without a calculator.

Find the domain of the function f(x)=9ln⁡(x−7)−6f(x)=\sqrt{9 \ln (x-7)}-6f(x)=9ln(x−7)​−6 .

A town with an initial population of 12,000 people doubles every 41 years. Determine the town's population after 12 years.

Consider the function f(x)=−55−x+2f(x)=-55^{-x}+2f(x)=−55−x+2 . A) Graph the function. B) State the domain. C) State all asymptotes.

Find a possible formula for the following graph using either logarithms or exponentials.

The following table gives zzz as a linear function of xxx . If z=ln⁡yz=\ln yz=lny , which of the following is a formula for yyy in terms of xxx ?

What annual interest rate, compounded monthly, is equivalent to an annual interest rate of 5.4% compounded continuously? Round your answer to the nearest thousandth of a percent, if necessary.

Let y=20e−0.07ty=20 e^{-0.07 t}y=20e−0.07t , with ttt measured in years. What is the continuous percent decay rate per year?

Let f(x)=log⁡(4x),g(x)=log⁡(2x)f(x)=\log (4 x), g(x)=\log (2 x)f(x)=log(4x),g(x)=log(2x) , and h(x)=f(x)−g(x)f(x)+g(x)h(x)=\frac{f(x)-g(x)}{f(x)+g(x)}h(x)=f(x)+g(x)f(x)−g(x)​ , with x>0x>0x>0 . Which of the following is a simplified formula for h(x)h(x)h(x) ?

Evaluate log⁡(105)\log (\sqrt[5]{10})log(510​) without a calculator. Leave fractions in the form "A\B" (do not convert to decimals).

How many times more powerful is an earthquake measuring 5.6 on the Richter scale than an earthquake measuring 4.5 on the Richter scale? Round your answer to two decimal places.

Evaluate log⁡(1019)\log \left(10^{19}\right)log(1019)

Let f(x)=log⁡(x−1)−1f(x)=\log (x-1)-1f(x)=log(x−1)−1 . A) Graph⁡f\operatorname{Graph} fGraphf . B) What are the asymptotes? C) What are the intercepts if they exist?

Let n=log⁡pn=\log pn=logp and m=log⁡qm=\log qm=logq . What is log⁡(p5q4)\log \left(p^{5} q^{4}\right)log(p5q4) ?

Rewriting 103=100010^{3}=1000103=1000 using logs gives

Find lim⁡x→6+ln⁡(x−6)\lim _{x \rightarrow 6^{+}} \ln (x-6)limx→6+​ln(x−6) .

Linear Functions and Change

Functions

Quadratic Functions

Exponential Functions

Transformations of Functions and Their Graphs

Trigonometry and Periodic Functions

Triangle Trigonometry and Polar Coordinates

Trigonometric Identities, Models, and Complex Numbers

Compositions, Inverses, and Combinations of Functions

Polynomial and Rational Functions

Vectors and Matrices

Sequences and Series

Parametric Equations and Conic Sections

Filters

Let $n=\log p$ and $m=\log q$ . What is $\log \frac{p^{6}}{q^{7}}$ ?

Let $n=\log p$ . What is $\log \sqrt[6]{p}$ ?

Does $\ln \left(x^{4} e^{-\ln \sqrt{x}}\right)=\frac{7}{2} \ln x$ ?

If $Q=\frac{1}{7} e^{0.062 t}$ is converted to the form $Q=a b^{t}$ , then $b=\ldots$ . Round to 3 decimal places.

Evaluate $e^{\ln \left(5^{2}\right)}$ without a calculator.

Find the domain of the function $f(x)=\sqrt{9 \ln (x-7)}-6$ .

Consider the function $f(x)=-55^{-x}+2$ . A) Graph the function. B) State the domain. C) State all asymptotes.

The following table gives $z$ as a linear function of $x$ . $The following table gives z as a linear function of x . If z=\ln y , which of the following is a formula for y in terms of x ?$ If $z=\ln y$ , which of the following is a formula for $y$ in terms of $x$ ?

Let $y=20 e^{-0.07 t}$ , with $t$ measured in years. What is the continuous percent decay rate per year?

Let $f(x)=\log (4 x), g(x)=\log (2 x)$ , and $h(x)=\frac{f(x)-g(x)}{f(x)+g(x)}$ , with $x>0$ . Which of the following is a simplified formula for $h(x)$ ?

Evaluate $\log (\sqrt[5]{10})$ without a calculator. Leave fractions in the form "A\B" (do not convert to decimals).

Evaluate $\log \left(10^{19}\right)$

Let $f(x)=\log (x-1)-1$ . A) $\operatorname{Graph} f$ . B) What are the asymptotes? C) What are the intercepts if they exist?

Let $n=\log p$ and $m=\log q$ . What is $\log \left(p^{5} q^{4}\right)$ ?

Rewriting $10^{3}=1000$ using logs gives

Find $\lim _{x \rightarrow 6^{+}} \ln (x-6)$ .