Question 1

Choose the one alternative that best completes the statement or answers the question.
Solve the equation.
-$$2 ^ { 2 x } = 4 ^ { x ^ { 2 } }$$
A) $\{ 0,1 \}$
B) $\left\{ \frac { 1 } { 2 } , - \frac { 1 } { 3 } \right\}$
C) $\{ 0 \}$
D) $\{ 4 \}$

Accepted Answer

The equation $2^{2x} = 4^{x^2}$ can be simplified by recognizing that $4$ is $2^2$. Thus, the equation becomes $2^{2x} = (2^2)^{x^2}$ or $2^{2x} = 2^{2x^2}$. For the bases and exponents to be equal, $2x = 2x^2$, leading to $x^2 - x = 0$, which factors to $x(x - 1) = 0$. The solutions are $x = 0$ and $x = 1$, making the correct choice $\{0,1\}$.

Question 2

Choose the one alternative that best completes the statement or answers the question.
Solve the equation.
-$$32 ^ { x + 5 } = 4 ^ { 3 x - 1 }$$
A) $\{ 12 \}$
B) $\{ 3 \}$
C) $\{ 27 \}$
D) \{ \}

Accepted Answer

The answer of Choose the one alternative that best completes...

Question 3

Determine if the statement is true or false.
-$\log _ { 4 } \left( \frac { 1 } { p } \right) = - \log _ { 4 } p$

Accepted Answer

The logarithmic identity $\log_b \left(\frac{1}{x}\right) = -\log_b x$ applies here, making the statement true.

Question 4

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-The equivalence property of exponential expressions indicates that if $b ^ { x } = b ^ { y }$ then = .

Accepted Answer

The answer of Write the word or phrase that best...

Question 5

Determine if the statement is true or false.
-$\log _ { 5 } \left( \frac { 1 } { x } \right) = \frac { 1 } { \log _ { 5 } x }$

Accepted Answer

The correct identity is $\log _ { 5 } \left( \frac { 1 } { x } \right) = -\log _ { 5 } x$, not the reciprocal of $\log _ { 5 } x$.

Question 6

Choose the one alternative that best completes the statement or answers the question.
Solve the equation.
-$$\left( \frac { 3 } { 4 } \right) ^ { 4 y + 6 } = \left( \frac { 9 } { 16 } \right) ^ { 5 y }$$
A) $\{ 0 \}$
B) $\{ 4 \}$
C) $\{ 1 \}$
D) No real solution

Accepted Answer

The answer of Choose the one alternative that best completes...

Question 7

Determine if the statement is true or false.
-$\log \left( \frac { x } { y } \right) = \frac { \log x } { \log y }$

Accepted Answer

The correct property is $\log \left( \frac { x } { y } \right) = \log x - \log y$, not division of the logarithms.

Question 8

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-An equation containing a variable within a logarithmic expression is called a equation.

Accepted Answer

The answer of Write the word or phrase that best...

Question 9

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-The equivalence property of logarithmic expressions indicates that if $\log _ { b } x = \log _ { b } y$ , then =
.

Accepted Answer

The answer of Write the word or phrase that best...

Question 10

Determine if the statement is true or false.
-$\log ( x y ) - ( \log x ) ( \log y )$

Accepted Answer

The expression does not simplify to an identity or a specific value universally; the subtraction of a logarithm of a product and the product of two logarithms does not result in a simplifiable or universally true statement.

Question 11

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-An equation such as $4 ^ { x } = 9$ is called an equation because the equation contains a variable
in the exponent.

Accepted Answer

The answer of Write the word or phrase that best...

Question 12

Choose the one alternative that best completes the statement or answers the question.
Solve the equation.
-$$5 ^ { 2 z + 3 } = 625$$
A) $\left\{ \frac { 1 } { 2 } \right\}$
B) $\{ 311 \}$
C) $\{ 4 \}$
D) $\left\{ \frac { 1 } { 5 } \right\}$

Accepted Answer

$$5^{2z+3} = 625$$ can be simplified to $$5^{2z+3} = 5^4$$ because $625 = 5^4$. Equating the exponents gives $2z + 3 = 4$, solving for $z$ gives $z = \frac{1}{2}$.

Question 13

Determine if the statement is true or false.
-$\ln 10 = \frac { 1 } { \log e }$

Accepted Answer

The answer of Determine if the statement is true or...

Question 14

Choose the one alternative that best completes the statement or answers the question.
Solve the equation.
-$\sqrt [ 5 ] { 49 } = 7 ^ { t }$
A) $\{ 10 \}$
B) $\left\{ \frac { 2 } { 5 } \right\}$
C) $\{ 5 \}$
D) $\left\{ \frac { 1 } { 5 } \right\}$

Accepted Answer

The equation $\sqrt[5]{49} = 7^t$ can be rewritten as $7^{\frac{2}{5}} = 7^t$, since $49 = 7^2$ and taking the fifth root is equivalent to raising to the power of $\frac{1}{5}$. Therefore, $t = \frac{2}{5}$.

Question 15

Choose the one alternative that best completes the statement or answers the question.
Solve the equation.
-$$9 ^ { x } = \frac { 1 } { 729 }$$
A) $\{ - 3 \}$
B) $\{ 3 \}$
C) $\left\{ \frac { 1 } { 3 } \right\}$
D) $\left\{ - \frac { 1 } { 3 } \right\}$

Accepted Answer

$$9^x = \frac{1}{729}$$ can be rewritten as $9^x = 9^{-3}$ because $729 = 9^3$, and thus $x = -3$.

Question 16

Choose the one alternative that best completes the statement or answers the question.
Solve the equation.
-$$4 ^ { ( 3 x + 3 ) } = \left( \frac { 1 } { 64 } \right) ^ { ( x - 9 ) }$$
A) - 2
B) 4
C) $- 4$
D) 2

Accepted Answer

The answer of Choose the one alternative that best completes...

Question 17

Choose the one alternative that best completes the statement or answers the question.
Solve the equation.
-$49 ^ { x + 8 } = 7 ^ { 4 x }$
A) $\{ 8 \}$
B) $\left\{ \frac { 10 } { 3 } \right\}$
C) $\left\{ - \frac { 56 } { 3 } \right\}$
D) No solution

Accepted Answer

The answer of Choose the one alternative that best completes...

Question 18

Determine if the statement is true or false.
-$\log _ { 2 } ( 7 y ) + \log _ { 2 } 2 = \log _ { 2 } ( 7 y )$

Accepted Answer

Using the product rule of logarithms, $\log _ { 2 } ( 7 y ) + \log _ { 2 } 2 = \log _ { 2 } ( 7 y \cdot 2 ) = \log _ { 2 } ( 14 y )$. Since $14 y \neq 7 y$, the statement is false.

Question 19

Choose the one alternative that best completes the statement or answers the question.
Solve the equation.
-$$5 ^ { 2 y } = 625$$
A) $\{ 4 \}$
B) $\{ 25 \}$
C) $\{ 2 \}$
D) $\{ 3 \}$

Accepted Answer

The answer of Choose the one alternative that best completes...

Question 20

Choose the one alternative that best completes the statement or answers the question.
Solve the equation.
-$$10,000 ^ { 4 x + 5 } = 10 ^ { 4 - x }$$
A) $- \frac { 1 } { 17 }$
B) $- \frac { 1 } { 5 }$
C) $- \frac { 16 } { 17 }$
D) $- \frac { 17 } { 16 }$

Accepted Answer

The answer of Choose the one alternative that best completes...

Quiz 4: Exponential and Logarithmic Functions

Choose the one alternative that best completes the statement or answers the question. Solve the equation. - $2 ^ { 2 x } = 4 ^ { x ^ { 2 } }$

Choose the one alternative that best completes the statement or answers the question. Solve the equation. - $32 ^ { x + 5 } = 4 ^ { 3 x - 1 }$

Determine if the statement is true or false. - $\log _ { 4 } \left( \frac { 1 } { p } \right) = - \log _ { 4 } p$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -The equivalence property of exponential expressions indicates that if $b ^ { x } = b ^ { y }$ then = .

Determine if the statement is true or false. - $\log _ { 5 } \left( \frac { 1 } { x } \right) = \frac { 1 } { \log _ { 5 } x }$

Choose the one alternative that best completes the statement or answers the question. Solve the equation. - $\left( \frac { 3 } { 4 } \right) ^ { 4 y + 6 } = \left( \frac { 9 } { 16 } \right) ^ { 5 y }$

Determine if the statement is true or false. - $\log \left( \frac { x } { y } \right) = \frac { \log x } { \log y }$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -An equation containing a variable within a logarithmic expression is called a equation.

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -The equivalence property of logarithmic expressions indicates that if $\log _ { b } x = \log _ { b } y$ , then = .

Determine if the statement is true or false. - $\log ( x y ) - ( \log x ) ( \log y )$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -An equation such as $4 ^ { x } = 9$ is called an equation because the equation contains a variable in the exponent.

Choose the one alternative that best completes the statement or answers the question. Solve the equation. - $5 ^ { 2 z + 3 } = 625$

Determine if the statement is true or false. - $\ln 10 = \frac { 1 } { \log e }$

Choose the one alternative that best completes the statement or answers the question. Solve the equation. - $\sqrt [ 5 ] { 49 } = 7 ^ { t }$

Choose the one alternative that best completes the statement or answers the question. Solve the equation. - $9 ^ { x } = \frac { 1 } { 729 }$

Choose the one alternative that best completes the statement or answers the question. Solve the equation. - $4 ^ { ( 3 x + 3 ) } = \left( \frac { 1 } { 64 } \right) ^ { ( x - 9 ) }$

Choose the one alternative that best completes the statement or answers the question. Solve the equation. - $49 ^ { x + 8 } = 7 ^ { 4 x }$

Determine if the statement is true or false. - $\log _ { 2 } ( 7 y ) + \log _ { 2 } 2 = \log _ { 2 } ( 7 y )$

Choose the one alternative that best completes the statement or answers the question. Solve the equation. - $5 ^ { 2 y } = 625$

Choose the one alternative that best completes the statement or answers the question. Solve the equation. - $10,000 ^ { 4 x + 5 } = 10 ^ { 4 - x }$

Quiz 4: Exponential and Logarithmic Functions

Choose the one alternative that best completes the statement or answers the question. Solve the equation. - 22x=4x22 ^ { 2 x } = 4 ^ { x ^ { 2 } }22x=4x2

Choose the one alternative that best completes the statement or answers the question. Solve the equation. - 32x+5=43x−132 ^ { x + 5 } = 4 ^ { 3 x - 1 }32x+5=43x−1

Determine if the statement is true or false. - log⁡4(1p)=−log⁡4p\log _ { 4 } \left( \frac { 1 } { p } \right) = - \log _ { 4 } plog4​(p1​)=−log4​p

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -The equivalence property of exponential expressions indicates that if bx=byb ^ { x } = b ^ { y }bx=by then = .

Determine if the statement is true or false. - log⁡5(1x)=1log⁡5x\log _ { 5 } \left( \frac { 1 } { x } \right) = \frac { 1 } { \log _ { 5 } x }log5​(x1​)=log5​x1​

Choose the one alternative that best completes the statement or answers the question. Solve the equation. - (34) 4y+6=(916) 5y\left( \frac { 3 } { 4 } \right) ^ { 4 y + 6 } = \left( \frac { 9 } { 16 } \right) ^ { 5 y }(43​) 4y+6=(169​) 5y

Determine if the statement is true or false. - log⁡(xy)=log⁡xlog⁡y\log \left( \frac { x } { y } \right) = \frac { \log x } { \log y }log(yx​)=logylogx​

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -An equation containing a variable within a logarithmic expression is called a equation.

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -The equivalence property of logarithmic expressions indicates that if log⁡bx=log⁡by\log _ { b } x = \log _ { b } ylogb​x=logb​y , then = .

Determine if the statement is true or false. - log⁡(xy)−(log⁡x)(log⁡y)\log ( x y ) - ( \log x ) ( \log y )log(xy)−(logx)(logy)

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -An equation such as 4x=94 ^ { x } = 94x=9 is called an equation because the equation contains a variable in the exponent.

Choose the one alternative that best completes the statement or answers the question. Solve the equation. - 52z+3=6255 ^ { 2 z + 3 } = 62552z+3=625

Determine if the statement is true or false. - ln⁡10=1log⁡e\ln 10 = \frac { 1 } { \log e }ln10=loge1​

Choose the one alternative that best completes the statement or answers the question. Solve the equation. - 495=7t\sqrt [ 5 ] { 49 } = 7 ^ { t }549​=7t

Choose the one alternative that best completes the statement or answers the question. Solve the equation. - 9x=17299 ^ { x } = \frac { 1 } { 729 }9x=7291​

Choose the one alternative that best completes the statement or answers the question. Solve the equation. - 4(3x+3) =(164) (x−9) 4 ^ { ( 3 x + 3 ) } = \left( \frac { 1 } { 64 } \right) ^ { ( x - 9 ) }4(3x+3) =(641​) (x−9)

Choose the one alternative that best completes the statement or answers the question. Solve the equation. - 49x+8=74x49 ^ { x + 8 } = 7 ^ { 4 x }49x+8=74x

Determine if the statement is true or false. - log⁡2(7y)+log⁡22=log⁡2(7y)\log _ { 2 } ( 7 y ) + \log _ { 2 } 2 = \log _ { 2 } ( 7 y )log2​(7y)+log2​2=log2​(7y)

Choose the one alternative that best completes the statement or answers the question. Solve the equation. - 52y=6255 ^ { 2 y } = 62552y=625

Choose the one alternative that best completes the statement or answers the question. Solve the equation. - 10,0004x+5=104−x10,000 ^ { 4 x + 5 } = 10 ^ { 4 - x }10,0004x+5=104−x

Choose the one alternative that best completes the statement or answers the question. Solve the equation. - $2 ^ { 2 x } = 4 ^ { x ^ { 2 } }$

Choose the one alternative that best completes the statement or answers the question. Solve the equation. - $32 ^ { x + 5 } = 4 ^ { 3 x - 1 }$

Determine if the statement is true or false. - $\log _ { 4 } \left( \frac { 1 } { p } \right) = - \log _ { 4 } p$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -The equivalence property of exponential expressions indicates that if $b ^ { x } = b ^ { y }$ then = .

Determine if the statement is true or false. - $\log _ { 5 } \left( \frac { 1 } { x } \right) = \frac { 1 } { \log _ { 5 } x }$

Choose the one alternative that best completes the statement or answers the question. Solve the equation. - $\left( \frac { 3 } { 4 } \right) ^ { 4 y + 6 } = \left( \frac { 9 } { 16 } \right) ^ { 5 y }$

Determine if the statement is true or false. - $\log \left( \frac { x } { y } \right) = \frac { \log x } { \log y }$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -The equivalence property of logarithmic expressions indicates that if $\log _ { b } x = \log _ { b } y$ , then = .

Determine if the statement is true or false. - $\log ( x y ) - ( \log x ) ( \log y )$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -An equation such as $4 ^ { x } = 9$ is called an equation because the equation contains a variable in the exponent.

Choose the one alternative that best completes the statement or answers the question. Solve the equation. - $5 ^ { 2 z + 3 } = 625$

Determine if the statement is true or false. - $\ln 10 = \frac { 1 } { \log e }$

Choose the one alternative that best completes the statement or answers the question. Solve the equation. - $\sqrt [ 5 ] { 49 } = 7 ^ { t }$

Choose the one alternative that best completes the statement or answers the question. Solve the equation. - $9 ^ { x } = \frac { 1 } { 729 }$

Choose the one alternative that best completes the statement or answers the question. Solve the equation. - $4 ^ { ( 3 x + 3 ) } = \left( \frac { 1 } { 64 } \right) ^ { ( x - 9 ) }$

Choose the one alternative that best completes the statement or answers the question. Solve the equation. - $49 ^ { x + 8 } = 7 ^ { 4 x }$

Determine if the statement is true or false. - $\log _ { 2 } ( 7 y ) + \log _ { 2 } 2 = \log _ { 2 } ( 7 y )$

Choose the one alternative that best completes the statement or answers the question. Solve the equation. - $5 ^ { 2 y } = 625$

Choose the one alternative that best completes the statement or answers the question. Solve the equation. - $10,000 ^ { 4 x + 5 } = 10 ^ { 4 - x }$