Question 1

Solve the logarithmic equation $\log _ { 7 } ( x - 4 ) + \log _ { 7 } ( x + 2 ) = 1$ for $x$ .

Accepted Answer

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Question 2

Evaluate the expression. $\log _ { 2 } 192 - \log _ { 2 } 3$

Accepted Answer

A)  $3$ 
B)  $4$ 
C)  $5$ 
D)  $6$ 
E)  $7$ 
A)  $3$ 
B)  $4$ 
C)  $5$ 
D)  $6$ 
E)  $7$

Question 3

The time required to double the amount of an investment at an interest rate r compounded continuously is given by $t = \frac { \ln 2 } {r }$ Find the time required to double an investment at 4%, 5%, and 6%.

Accepted Answer

17.3 yr, 1

Question 4

If one earthquake is $5$ times as intense as another, how much larger is its magnitude on the Richter Scale?

Accepted Answer

@#LAT-DLM& @#LAT-DLM& @#LAT-DLM& . So it

Question 5

A 16-g sample of radioactive iodine decays in such a way that the mass remaining after t days is given by $m ( t ) = 16 e ^ { - 0087 t }$ , where $m ( t )$ is measured in grams. After how many days is there only 4 g remaining?

Accepted Answer

The answer of A 16-g sample of radioactive iodine decays...

Question 6

How long will it take for an investment of $\$ 2550$ to double in value if the interest rate is $5.65 \%$ per year compounded continuously?

Accepted Answer

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Question 7

Use the definition of the logarithmic function to find $x$ if $\log _ { x } 7 = 1 / 3$ .

Accepted Answer

The answer of Use the definition of the logarithmic function...

Question 8

Use the definition of the logarithmic function to find $x$ if $\log _ { 3 } 27 = x$ .

Accepted Answer

The answer of Use the definition of the logarithmic function...

Question 9

Express the equation $6 ^ { 3 } = 216$ in logarithmic form.

Accepted Answer

A)  $\log _ { 2 } 216 = 3$ 
B)  $\log _ { 3 } 216 = 6$ 
C)  $\log _ { 6 } 216 = 3$ 
D)  $\log _ { 6 } 216 = 36$ 
E)  $\log _ { 6 } 36 = 2$ 
A)  $\log _ { 2 } 216 = 3$ 
B)  $\log _ { 3 } 216 = 6$ 
C)  $\log _ { 6 } 216 = 3$ 
D)  $\log _ { 6 } 216 = 36$ 
E)  $\log _ { 6 } 36 = 2$

Question 10

Evaluate the expression. $\log _ { 3 } 81 ^ { 22 }$

Accepted Answer

The answer of Evaluate the expression. \(\log _ { 3...

Question 11

How much more intense is an earthquake with a magnitude of $5.4$ on the Richter scale than one with a magnitude of $3.2$ ?

Accepted Answer

@#LAT-DLM& . So it i

Question 12

Sketch the graph of the function $f ( x ) = \left( \frac { 3 } { 2 } \right) ^ { x }$ by making a table of values. Use a calculator if necessary.

Accepted Answer

The answer of Sketch the graph of the function \(f...

Question 13

Express the equation $\log _ { 13 } 1 = 0$ in exponential form.

Accepted Answer

A)  $13 ^ { 1} = 0$ 
B)  $0 ^ { 13 } = 1$ 
C)  $13 ^ { \mathrm { D } } = 1$ 
D)  $1 ^ { 13 } = 1$ 
E)  $13 ^ { 1 } = 13$ 
A)  $13 ^ { 1} = 0$ 
B)  $0 ^ { 13 } = 1$ 
C)  $13 ^ { \mathrm { D } } = 1$ 
D)  $1 ^ { 13 } = 1$ 
E)  $13 ^ { 1 } = 13$

Question 14

The frog population in a pond grows exponentially. The current population is $235$ frogs, and the relative growth rate is $12 \%$ per year.
(a) Find a formula for the population $n ( t )$ after $t$ years.
(b) Find the projected population after $5$ years.
(c) Find the number of years required for the frog population to reach $1000$ .

Accepted Answer

(a) @#LAT-DLM&
(b) @#LAT-DLM&

Question 15

The intensity level of sound at a crowded football game was measured at $96$ dB. Find the intensity in watts/m   .

Accepted Answer

The answer of The intensity level of sound at a...

Question 16

Use the Laws of Logarithms to rewrite $\ln ( e / x )$ in a form with no logarithms of products, quotients, or powers.

Accepted Answer

A)  $2 + 2 \ln x$ 
B)  $1 - \ln x$ 
C)  $e \ln x$ 
D)  $- \ln x$ 
E)  $1 + \ln x$ 
A)  $2 + 2 \ln x$ 
B)  $1 - \ln x$ 
C)  $e \ln x$ 
D)  $- \ln x$ 
E)  $1 + \ln x$

Question 17

Graph the function $g ( x ) = 2 ^ { x + 1 }$ , not by plotting points but by applying your knowledge of the general shape of graphs of the form $a ^ { x }$ . State the domain, range, and asymptote of the function.

Accepted Answer

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

Question 18

If $2500 is invested at an interest rate of 6.25% per year, compounded continuously, find the value of the investment after the given number of years.
(a) 3 years
(b) 6 years
(c) 9 years

Accepted Answer

a) $3015.5

Question 19

Use a calculator to evaluate the expression $\log 13$ to four decimal places.

Accepted Answer

A)  $1.2465$ 
B)  $1.5493$ 
C)  $1.6489$ 
D)  $1.9954$ 
E)  $1.1139$ 
A)  $1.2465$ 
B)  $1.5493$ 
C)  $1.6489$ 
D)  $1.9954$ 
E)  $1.1139$

Solve the logarithmic equation $\log _ { 7 } ( x - 4 ) + \log _ { 7 } ( x + 2 ) = 1$ for $x$ .

Evaluate the expression. $\log _ { 2 } 192 - \log _ { 2 } 3$

The time required to double the amount of an investment at an interest rate r compounded continuously is given by $t = \frac { \ln 2 } {r }$ Find the time required to double an investment at 4%, 5%, and 6%.

If one earthquake is $5$ times as intense as another, how much larger is its magnitude on the Richter Scale?

A 16-g sample of radioactive iodine decays in such a way that the mass remaining after t days is given by $m ( t ) = 16 e ^ { - 0087 t }$ , where $m ( t )$ is measured in grams. After how many days is there only 4 g remaining?

How long will it take for an investment of $\$ 2550$ to double in value if the interest rate is $5.65 \%$ per year compounded continuously?

Use the definition of the logarithmic function to find $x$ if $\log _ { x } 7 = 1 / 3$ .

Use the definition of the logarithmic function to find $x$ if $\log _ { 3 } 27 = x$ .

Express the equation $6 ^ { 3 } = 216$ in logarithmic form.

Evaluate the expression. $\log _ { 3 } 81 ^ { 22 }$

How much more intense is an earthquake with a magnitude of $5.4$ on the Richter scale than one with a magnitude of $3.2$ ?

Sketch the graph of the function $f ( x ) = \left( \frac { 3 } { 2 } \right) ^ { x }$ by making a table of values. Use a calculator if necessary.

Express the equation $\log _ { 13 } 1 = 0$ in exponential form.

The intensity level of sound at a crowded football game was measured at $96$ dB. Find the intensity in watts/m .

Use the Laws of Logarithms to rewrite $\ln ( e / x )$ in a form with no logarithms of products, quotients, or powers.

Graph the function $g ( x ) = 2 ^ { x + 1 }$ , not by plotting points but by applying your knowledge of the general shape of graphs of the form $a ^ { x }$ . State the domain, range, and asymptote of the function.

If $2500 is invested at an interest rate of 6.25% per year, compounded continuously, find the value of the investment after the given number of years. (a) 3 years (b) 6 years (c) 9 years

Use a calculator to evaluate the expression $\log 13$ to four decimal places.

Fundamentals

Functions

Polynomial and Rational Functions

Trigonometric Functions: Unit Circle Approach

Trigonometric Functions: Right Triangle Approach

Analytic Trigonometry

Polar Coordinates and Parametric Equations

Vectors in Two and Three Dimensions

Systems of Equations and Inequalities

Conic Sections

Sequences and Series

Limits: a Preview of Calculus

Filters

Exam 4: Exponential and Logarithmic Functions

Solve the logarithmic equation log⁡7(x−4)+log⁡7(x+2)=1\log _ { 7 } ( x - 4 ) + \log _ { 7 } ( x + 2 ) = 1log7​(x−4)+log7​(x+2)=1 for xxx .

Evaluate the expression. log⁡2192−log⁡23\log _ { 2 } 192 - \log _ { 2 } 3log2​192−log2​3

The time required to double the amount of an investment at an interest rate r compounded continuously is given by t=ln⁡2rt = \frac { \ln 2 } {r }t=rln2​ Find the time required to double an investment at 4%, 5%, and 6%.

If one earthquake is 555 times as intense as another, how much larger is its magnitude on the Richter Scale?

A 16-g sample of radioactive iodine decays in such a way that the mass remaining after t days is given by m(t)=16e−0087tm ( t ) = 16 e ^ { - 0087 t }m(t)=16e−0087t , where m(t)m ( t )m(t) is measured in grams. After how many days is there only 4 g remaining?

How long will it take for an investment of $2550\$ 2550$2550 to double in value if the interest rate is 5.65%5.65 \%5.65% per year compounded continuously?

Use the definition of the logarithmic function to find xxx if log⁡x7=1/3\log _ { x } 7 = 1 / 3logx​7=1/3 .

Use the definition of the logarithmic function to find xxx if log⁡327=x\log _ { 3 } 27 = xlog3​27=x .

Express the equation 63=2166 ^ { 3 } = 21663=216 in logarithmic form.

Evaluate the expression. log⁡38122\log _ { 3 } 81 ^ { 22 }log3​8122

How much more intense is an earthquake with a magnitude of 5.45.45.4 on the Richter scale than one with a magnitude of 3.23.23.2 ?

Sketch the graph of the function f(x)=(32)xf ( x ) = \left( \frac { 3 } { 2 } \right) ^ { x }f(x)=(23​)x by making a table of values. Use a calculator if necessary.

Express the equation log⁡131=0\log _ { 13 } 1 = 0log13​1=0 in exponential form.

The intensity level of sound at a crowded football game was measured at 969696 dB. Find the intensity in watts/m .

Use the Laws of Logarithms to rewrite ln⁡(e/x)\ln ( e / x )ln(e/x) in a form with no logarithms of products, quotients, or powers.

Graph the function g(x)=2x+1g ( x ) = 2 ^ { x + 1 }g(x)=2x+1 , not by plotting points but by applying your knowledge of the general shape of graphs of the form axa ^ { x }ax . State the domain, range, and asymptote of the function.

If $2500 is invested at an interest rate of 6.25% per year, compounded continuously, find the value of the investment after the given number of years. (a) 3 years (b) 6 years (c) 9 years

Use a calculator to evaluate the expression log⁡13\log 13log13 to four decimal places.

Fundamentals

Functions

Polynomial and Rational Functions

Trigonometric Functions: Unit Circle Approach

Trigonometric Functions: Right Triangle Approach

Analytic Trigonometry

Polar Coordinates and Parametric Equations

Vectors in Two and Three Dimensions

Systems of Equations and Inequalities

Conic Sections

Sequences and Series

Limits: a Preview of Calculus

Filters

Solve the logarithmic equation $\log _ { 7 } ( x - 4 ) + \log _ { 7 } ( x + 2 ) = 1$ for $x$ .

Evaluate the expression. $\log _ { 2 } 192 - \log _ { 2 } 3$

The time required to double the amount of an investment at an interest rate r compounded continuously is given by $t = \frac { \ln 2 } {r }$ Find the time required to double an investment at 4%, 5%, and 6%.

If one earthquake is $5$ times as intense as another, how much larger is its magnitude on the Richter Scale?

A 16-g sample of radioactive iodine decays in such a way that the mass remaining after t days is given by $m ( t ) = 16 e ^ { - 0087 t }$ , where $m ( t )$ is measured in grams. After how many days is there only 4 g remaining?

How long will it take for an investment of $\$ 2550$ to double in value if the interest rate is $5.65 \%$ per year compounded continuously?

Use the definition of the logarithmic function to find $x$ if $\log _ { x } 7 = 1 / 3$ .

Use the definition of the logarithmic function to find $x$ if $\log _ { 3 } 27 = x$ .

Express the equation $6 ^ { 3 } = 216$ in logarithmic form.

Evaluate the expression. $\log _ { 3 } 81 ^ { 22 }$

How much more intense is an earthquake with a magnitude of $5.4$ on the Richter scale than one with a magnitude of $3.2$ ?

Sketch the graph of the function $f ( x ) = \left( \frac { 3 } { 2 } \right) ^ { x }$ by making a table of values. Use a calculator if necessary.

Express the equation $\log _ { 13 } 1 = 0$ in exponential form.

The intensity level of sound at a crowded football game was measured at $96$ dB. Find the intensity in watts/m .

Use the Laws of Logarithms to rewrite $\ln ( e / x )$ in a form with no logarithms of products, quotients, or powers.

Graph the function $g ( x ) = 2 ^ { x + 1 }$ , not by plotting points but by applying your knowledge of the general shape of graphs of the form $a ^ { x }$ . State the domain, range, and asymptote of the function.

Use a calculator to evaluate the expression $\log 13$ to four decimal places.