What is the value of A when we rewrite 3^(x) as A^(5x) ? Choose 1 answer: (A) A=3 (B) A=3^(-5) (c) A=3^((1)/(5)) (D) A=3^(-(1)/(5))

Given equation: We are given the equation 3^(x) and we want to express it in the form A^(5x). To do this, we need to find a value for A such that raising A to the power of 5x will give us the same result as raising 3 to the power of x.Equating the expressions: We can start by equating the two expressions: 3^(x) = A^(5x) Since the bases must be the same for the exponents to be equal, we can deduce that A^5 must be equal to 3.Finding A: To find A, we take the fifth root of both sides of the equation A^5 = 3: A = (3)^(1/5) This simplifies to A being the fifth root of 3.Checking the answer choices: Now we can check the answer choices to see which one matches our result: (A) A=3 (This would imply A^5 = 3^5, which is not correct.) (B) A=3^(-5) (This would imply A^5 = (3^(-5))^5 = 3^(-25), which is not correct.) (C) A=3^(1/5) (This matches our result, so it is correct.) (D) A=3^(-1/5) (This would imply A^5 = (3^(-1/5))^5 = 3^(-1), which is not correct.)

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What is the value of
A when we rewrite
3^(x) as
A^(5x) ?
Choose 1 answer:
(A)
A=3
(B)
A=3^(-5)
(c)
A=3^((1)/(5))
(D)
A=3^(-(1)/(5))

What is the value of $A$ when we rewrite $3^{x}$ as $A^{5 x}$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $A=3$ $\newline$ (B) $A=3^{-5}$ $\newline$ (C) $A=3^{\frac{1}{5}}$ $\newline$ (D) $A=3^{-\frac{1}{5}}$

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Math Problems

Algebra 1

Compare linear and exponential growth

Full solution

Q. What is the value of

A

when we rewrite

3^{x}

A^{5 x}

\newline

Choose

1

answer:

\newline

(A)

A=3

\newline

(B)

A=3^{-5}

\newline

(C)

A=3^{\frac{1}{5}}

\newline

(D)

A=3^{-\frac{1}{5}}

Given equation: We are given the equation $3^{x}$ and we want to express it in the form $A^{5x}$ . To do this, we need to find a value for $A$ such that raising $A$ to the power of $5x$ will give us the same result as raising $3$ to the power of $x$ .
Equating the expressions: We can start by equating the two expressions: $\newline$ $3^{x} = A^{5x}$ $\newline$ Since the bases must be the same for the exponents to be equal, we can deduce that $A^5$ must be equal to $3$ .
Finding A: To find $A$ , we take the fifth root of both sides of the equation $A^5 = 3$ : $\newline$ $A = (3)^{(1/5)}$ $\newline$ This simplifies to $A$ being the fifth root of $3$ .
Checking the answer choices: Now we can check the answer choices to see which one matches our result: $\newline$ (A) $A=3$ (This would imply $A^5 = 3^5$ , which is not correct.) $\newline$ (B) $A=3^{-5}$ (This would imply $A^5 = (3^{-5})^5 = 3^{-25}$ , which is not correct.) $\newline$ (C) $A=3^{\frac{1}{5}}$ (This matches our result, so it is correct.) $\newline$ (D) $A=3^{-\frac{1}{5}}$ (This would imply $A^5 = (3^{-\frac{1}{5}})^5 = 3^{-1}$ , which is not correct.)