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What is the value of
A when we rewrite
29^((x)/(2)) as
A^(x) ?
Choose 1 answer:
(A)
A=(29)/(2)
(B)
A=29^(2)
(C)
A=29^((1)/(2))
(D)
A=((1)/(29))^(2)

What is the value of $A$ when we rewrite $29^{\frac{x}{2}}$ as $A^{x}$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $A=\frac{29}{2}$ $\newline$ (B) $A=29^{2}$ $\newline$ (C) $A=29^{\frac{1}{2}}$ $\newline$ (D) $A=\left(\frac{1}{29}\right)^{2}$

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Compare linear and exponential growth

Full solution

Q. What is the value of

A

when we rewrite

29^{\frac{x}{2}}

as

A^{x}

?

\newline

Choose

1

answer:

\newline

(A)

A=\frac{29}{2}

\newline

(B)

A=29^{2}

\newline

(C)

A=29^{\frac{1}{2}}

\newline

(D)

A=\left(\frac{1}{29}\right)^{2}

Find Base A: To rewrite $29^{(x/2)}$ as $A^x$ , we need to find a base $A$ such that when raised to the power of $x$ , it is equivalent to $29^{(x/2)}$ . This means we are looking for a base $A$ that when squared (because the exponent $x$ in $A^x$ will be effectively halved when compared to $29^{(x/2)}$ ) gives us $29$ .
Square of A: We know that $(A^{x})^2 = A^{2x}$ . Therefore, if we want $A^{x}$ to be equivalent to $29^{\frac{x}{2}}$ , we need $A^2$ to be equal to $29$ . This means $A$ is the square root of $29$ .
Calculate A: The square root of $29$ is written as $29^{(\frac{1}{2})}$ . Therefore, $A = 29^{(\frac{1}{2})}$ .
Check Answer Choices: We can now check the answer choices to see which one matches our result: $\newline$ (A) $A=\frac{29}{2}$ is incorrect because it represents a fraction, not a square root. $\newline$ (B) $A=29^{2}$ is incorrect because it represents the square of $29$ , not the square root. $\newline$ (C) $A=29^{\frac{1}{2}}$ is correct because it represents the square root of $29$ . $\newline$ (D) $A=\left(\frac{1}{29}\right)^{2}$ is incorrect because it represents the square of the reciprocal of $29$ , not the square root of $29$ .

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f(x)

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