Question 1

Solve the equation. ${ } ^ { 227 } \mathrm { Th }$

Accepted Answer

The answer of Solve the equation. \({ } ^ {...

Question 2

Find the inverse of the function and express it using $f ^ { - 1 } ( x )$ notation. $f ( x ) = \frac { 2 x + 4 } { 3 }$

Accepted Answer

The answer of Find the inverse of the function and...

Question 3

Use change of base theorem to evaluate $\log _ { \frac { 1 } { 4 } } 12$ . Round the answer to four decimal places.

Accepted Answer

A)  $- 0.5579$ 
B)  $- 1.7925$ 
C)  0.7925 
D)  -0.4421 
A)  $- 0.5579$ 
B)  $- 1.7925$ 
C)  0.7925 
D)  -0.4421

Question 4

Use composition to show that the pair of functions are inverses. $f ( x ) = 3 x + 7 , f ^ { - 1 } ( x ) = \frac { x - 7 } { 3 }$

Accepted Answer

@#IMG-DLM&  ,@#IMG-DLM& Becaus

Question 5

Evaluate: $\ln \sqrt [ 6 ] { e }$

Accepted Answer

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

Question 6

An isotope of thorium, ${ } ^ { 227 } \mathrm { Th }$ , has a half-life of 18.4 days. How long will it take for 79% of the sample to decompose?
 Please round the answer to the nearest tenth. __________ days

Accepted Answer

The answer of An isotope of thorium, \({ } ^...

Question 7

An account now contains $11150 and has been accumulating interest at 7.2% annual interest, compounded continuously, for 7 years. Find the initial deposit. Please round the answer to the nearest cent. $__________

Accepted Answer

The answer of An account now contains $11150 and has...

Question 8

Let $f ( x ) = 5 x + 4$ and $g ( x ) = x ^ { 2 } - 2$ . Find the composition. $( f \circ g ) ( 3 )$

Accepted Answer

The answer of Let \(f ( x ) = 5...

Question 9

To solve $7 ^ { x } = 3$ , we can take the _________ of both sides of the equation to get $\log 7 ^ { x } = \log 3$ .

Accepted Answer

The answer of To solve \(7 ^ { x }...

Question 10

Use the properties of logarithms to write $5 \log _ { 5 } ( x - 2 ) - \log _ { 5 } x$ as a single logarithm. Assume x is a positive number.

Accepted Answer

A)  $\frac { \log _ { 5 } ( x - 2 ) ^ { 5 } } { \log _ { 5 } x }$ 
B)  $\log _ { 5 } \frac { ( x - 2 ) ^ { 5 } } { x }$ 
C)  $\log _ { 5 } x ( x - 2 ) ^ { 5 }$ 
D)  $\log _ { 5 } \left( \frac { x - 2 } { x } \right) ^ { 5 }$ 
A)  $\frac { \log _ { 5 } ( x - 2 ) ^ { 5 } } { \log _ { 5 } x }$ 
B)  $\log _ { 5 } \frac { ( x - 2 ) ^ { 5 } } { x }$ 
C)  $\log _ { 5 } x ( x - 2 ) ^ { 5 }$ 
D)  $\log _ { 5 } \left( \frac { x - 2 } { x } \right) ^ { 5 }$

Question 11

Determine whether the function $f ( x ) = | x + 5 |$ is one-to-one.

Accepted Answer

A)  one-to-one 
B)  not one-to-one 
A)  one-to-one 
B)  not one-to-one

Question 12

A function is called a __________ function if different inputs determine different outputs.

Accepted Answer

The answer of A function is called a __________ function...

Question 13

Evaluate the expression. $\log 1000$

Accepted Answer

The answer of Evaluate the expression. $\log 1000$...

Question 14

Evaluate: $\ln \sqrt [ 6 ] { e ^ { 7 } }$

Accepted Answer

A)  7 
B)  6 
C)  $\frac { 7 } { 6 }$ 
D)  $\frac { 6 } { 7 }$ 
A)  7 
B)  6 
C)  $\frac { 7 } { 6 }$ 
D)  $\frac { 6 } { 7 }$

Question 15

Let $f ( x ) = 3 x - 4$ and $g ( x ) = x ^ { 2 } - 1$ . Find: $( g \circ f ) ( - 1 )$

Accepted Answer

A)  -4 
B)  0 
C)  $- 3 x ^ { 2 } + 24 x - 15$ 
D)  48 
A)  -4 
B)  0 
C)  $- 3 x ^ { 2 } + 24 x - 15$ 
D)  48

Question 16

Solve each equation. ${ } ^ { 227 } \mathrm { Th }$

Accepted Answer

The answer of Solve each equation. \({ } ^ {...

Question 17

If the function $f ( x ) = \frac { x + 9 } { 5 }$ is one-to-one, find its inverse.

Accepted Answer

A)  $f ^ { - 1 } ( x ) = \frac { 5 } { x + 9 }$ 
B)  $f ^ { - 1 } ( x ) = 5 x - 9$ 
C)  $f ^ { - 1 } ( x ) = 5 x + 9$ 
D)  not one-to-one 
A)  $f ^ { - 1 } ( x ) = \frac { 5 } { x + 9 }$ 
B)  $f ^ { - 1 } ( x ) = 5 x - 9$ 
C)  $f ^ { - 1 } ( x ) = 5 x + 9$ 
D)  not one-to-one

Question 18

Simplify the expression. Write answer using only positive exponents. $\left( 2 ^ { \sqrt { 12 } } \right) ^ { \sqrt { 3 } }$

Accepted Answer

The answer of Simplify the expression. Write answer using only...

Question 19

Assume that $\log _ { b } 4 = 0.6061$ and $\log _ { b } 9 = 0.9082$ Use these values and properties of logarithms to find $\log _ { b } 36$ . Round your answers to four decimal places.

Accepted Answer

A)  $- 0.3021$ 
B)  0.3021 
C)  0.5505 
D)  1.5143 
A)  $- 0.3021$ 
B)  0.3021 
C)  0.5505 
D)  1.5143

Question 20

Write the logarithm as a sum and/or difference of logarithms of a single quantity. Then simplify if possible. Assume that q , w , r , and b are positive numbers, and $b \neq 1$ . $\log _ { b } \sqrt [ 4 ] { \frac { q ^ { 3 } w ^ { 2 } } { r ^ { 4 } } }$

Accepted Answer

The answer of Write the logarithm as a sum and/or...

Solve the equation. ${ } ^ { 227 } \mathrm { Th }$

Find the inverse of the function and express it using $f ^ { - 1 } ( x )$ notation. $f ( x ) = \frac { 2 x + 4 } { 3 }$

Use change of base theorem to evaluate $\log _ { \frac { 1 } { 4 } } 12$ . Round the answer to four decimal places.

Use composition to show that the pair of functions are inverses. $f ( x ) = 3 x + 7 , f ^ { - 1 } ( x ) = \frac { x - 7 } { 3 }$

Evaluate: $\ln \sqrt [ 6 ] { e }$

An isotope of thorium, ${ } ^ { 227 } \mathrm { Th }$ , has a half-life of 18.4 days. How long will it take for 79% of the sample to decompose? Please round the answer to the nearest tenth. __________ days

An account now contains $11150 and has been accumulating interest at 7.2% annual interest, compounded continuously, for 7 years. Find the initial deposit. Please round the answer to the nearest cent. $__________

Let $f ( x ) = 5 x + 4$ and $g ( x ) = x ^ { 2 } - 2$ . Find the composition. $( f \circ g ) ( 3 )$

To solve $7 ^ { x } = 3$ , we can take the _________ of both sides of the equation to get $\log 7 ^ { x } = \log 3$ .

Use the properties of logarithms to write $5 \log _ { 5 } ( x - 2 ) - \log _ { 5 } x$ as a single logarithm. Assume x is a positive number.

Determine whether the function $f ( x ) = | x + 5 |$ is one-to-one.

A function is called a __________ function if different inputs determine different outputs.

Evaluate the expression. $\log 1000$

Evaluate: $\ln \sqrt [ 6 ] { e ^ { 7 } }$

Let $f ( x ) = 3 x - 4$ and $g ( x ) = x ^ { 2 } - 1$ . Find: $( g \circ f ) ( - 1 )$

Solve each equation. ${ } ^ { 227 } \mathrm { Th }$

If the function $f ( x ) = \frac { x + 9 } { 5 }$ is one-to-one, find its inverse.

Simplify the expression. Write answer using only positive exponents. $\left( 2 ^ { \sqrt { 12 } } \right) ^ { \sqrt { 3 } }$

Assume that $\log _ { b } 4 = 0.6061$ and $\log _ { b } 9 = 0.9082$ Use these values and properties of logarithms to find $\log _ { b } 36$ . Round your answers to four decimal places.

Write the logarithm as a sum and/or difference of logarithms of a single quantity. Then simplify if possible. Assume that q , w , r , and b are positive numbers, and $b \neq 1$ . $\log _ { b } \sqrt [ 4 ] { \frac { q ^ { 3 } w ^ { 2 } } { r ^ { 4 } } }$

A Review of Basic Algebra

Graphs, Equations of Lines, and Functions

Systems of Equations

Inequalities

Exponents, Polynomials, and Polynomial Functions

Rational Expression and Equations

Radical Expressions and Equations

Quadratic Equations, Functions, and Inequalities

Conic Sections; More Graphing

Miscellaneous Topics

Filters

Exam 9: Exponential and Logarithmic Functions

Solve the equation. 227Th{ } ^ { 227 } \mathrm { Th }227Th

Find the inverse of the function and express it using f−1(x)f ^ { - 1 } ( x )f−1(x) notation. f(x)=2x+43f ( x ) = \frac { 2 x + 4 } { 3 }f(x)=32x+4​

Use change of base theorem to evaluate log⁡1412\log _ { \frac { 1 } { 4 } } 12log41​​12 . Round the answer to four decimal places.

Use composition to show that the pair of functions are inverses. f(x)=3x+7,f−1(x)=x−73f ( x ) = 3 x + 7 , f ^ { - 1 } ( x ) = \frac { x - 7 } { 3 }f(x)=3x+7,f−1(x)=3x−7​

Evaluate: ln⁡e6\ln \sqrt [ 6 ] { e }ln6e​

An isotope of thorium, 227Th{ } ^ { 227 } \mathrm { Th }227Th , has a half-life of 18.4 days. How long will it take for 79% of the sample to decompose? Please round the answer to the nearest tenth. __________ days

An account now contains $11150 and has been accumulating interest at 7.2% annual interest, compounded continuously, for 7 years. Find the initial deposit. Please round the answer to the nearest cent. $__________

Let f(x)=5x+4f ( x ) = 5 x + 4f(x)=5x+4 and g(x)=x2−2g ( x ) = x ^ { 2 } - 2g(x)=x2−2 . Find the composition. (f∘g)(3)( f \circ g ) ( 3 )(f∘g)(3)

To solve 7x=37 ^ { x } = 37x=3 , we can take the _________ of both sides of the equation to get log⁡7x=log⁡3\log 7 ^ { x } = \log 3log7x=log3 .

Use the properties of logarithms to write 5log⁡5(x−2)−log⁡5x5 \log _ { 5 } ( x - 2 ) - \log _ { 5 } x5log5​(x−2)−log5​x as a single logarithm. Assume x is a positive number.

Determine whether the function f(x)=∣x+5∣f ( x ) = | x + 5 |f(x)=∣x+5∣ is one-to-one.

A function is called a __________ function if different inputs determine different outputs.

Evaluate the expression. log⁡1000\log 1000log1000

Evaluate: ln⁡e76\ln \sqrt [ 6 ] { e ^ { 7 } }ln6e7​

Let f(x)=3x−4f ( x ) = 3 x - 4f(x)=3x−4 and g(x)=x2−1g ( x ) = x ^ { 2 } - 1g(x)=x2−1 . Find: (g∘f)(−1)( g \circ f ) ( - 1 )(g∘f)(−1)

Solve each equation. 227Th{ } ^ { 227 } \mathrm { Th }227Th

If the function f(x)=x+95f ( x ) = \frac { x + 9 } { 5 }f(x)=5x+9​ is one-to-one, find its inverse.

Simplify the expression. Write answer using only positive exponents. (212)3\left( 2 ^ { \sqrt { 12 } } \right) ^ { \sqrt { 3 } }(212​)3​

Assume that log⁡b4=0.6061\log _ { b } 4 = 0.6061logb​4=0.6061 and log⁡b9=0.9082\log _ { b } 9 = 0.9082logb​9=0.9082 Use these values and properties of logarithms to find log⁡b36\log _ { b } 36logb​36 . Round your answers to four decimal places.

Write the logarithm as a sum and/or difference of logarithms of a single quantity. Then simplify if possible. Assume that q , w , r , and b are positive numbers, and b≠1b \neq 1b=1 . log⁡bq3w2r44\log _ { b } \sqrt [ 4 ] { \frac { q ^ { 3 } w ^ { 2 } } { r ^ { 4 } } }logb​4r4q3w2​​

A Review of Basic Algebra

Graphs, Equations of Lines, and Functions

Systems of Equations

Inequalities

Exponents, Polynomials, and Polynomial Functions

Rational Expression and Equations

Radical Expressions and Equations

Quadratic Equations, Functions, and Inequalities

Conic Sections; More Graphing

Miscellaneous Topics

Filters

Solve the equation. ${ } ^ { 227 } \mathrm { Th }$

Find the inverse of the function and express it using $f ^ { - 1 } ( x )$ notation. $f ( x ) = \frac { 2 x + 4 } { 3 }$

Use change of base theorem to evaluate $\log _ { \frac { 1 } { 4 } } 12$ . Round the answer to four decimal places.

Use composition to show that the pair of functions are inverses. $f ( x ) = 3 x + 7 , f ^ { - 1 } ( x ) = \frac { x - 7 } { 3 }$

Evaluate: $\ln \sqrt [ 6 ] { e }$

An isotope of thorium, ${ } ^ { 227 } \mathrm { Th }$ , has a half-life of 18.4 days. How long will it take for 79% of the sample to decompose? Please round the answer to the nearest tenth. __________ days

Let $f ( x ) = 5 x + 4$ and $g ( x ) = x ^ { 2 } - 2$ . Find the composition. $( f \circ g ) ( 3 )$

To solve $7 ^ { x } = 3$ , we can take the _________ of both sides of the equation to get $\log 7 ^ { x } = \log 3$ .

Use the properties of logarithms to write $5 \log _ { 5 } ( x - 2 ) - \log _ { 5 } x$ as a single logarithm. Assume x is a positive number.

Determine whether the function $f ( x ) = | x + 5 |$ is one-to-one.

Evaluate the expression. $\log 1000$

Evaluate: $\ln \sqrt [ 6 ] { e ^ { 7 } }$

Let $f ( x ) = 3 x - 4$ and $g ( x ) = x ^ { 2 } - 1$ . Find: $( g \circ f ) ( - 1 )$

Solve each equation. ${ } ^ { 227 } \mathrm { Th }$

If the function $f ( x ) = \frac { x + 9 } { 5 }$ is one-to-one, find its inverse.

Simplify the expression. Write answer using only positive exponents. $\left( 2 ^ { \sqrt { 12 } } \right) ^ { \sqrt { 3 } }$

Assume that $\log _ { b } 4 = 0.6061$ and $\log _ { b } 9 = 0.9082$ Use these values and properties of logarithms to find $\log _ { b } 36$ . Round your answers to four decimal places.

Write the logarithm as a sum and/or difference of logarithms of a single quantity. Then simplify if possible. Assume that q , w , r , and b are positive numbers, and $b \neq 1$ . $\log _ { b } \sqrt [ 4 ] { \frac { q ^ { 3 } w ^ { 2 } } { r ^ { 4 } } }$