What is the inverse of the function y=log_(3)x ? (1) y=x^(3) (2) y=log_(x)3 (3) y=3^(x) (4) x=3^(y)

Identify Function Components: Identify the original function and its components. The original function is y = log_(3)(x), which means that 3 raised to the power of y equals x.Write in Exponential Form: Write the original function in exponential form. To find the inverse, we switch x and y and solve for the new y. So, we rewrite the equation as x = 3^y.Solve for Inverse Function: Solve for the new y to express the inverse function. To express the inverse function, we solve for y, which gives us y = log_(3)(x). Since we have switched x and y, the inverse function is x = 3^y.Check Answer Choices: Check the answer choices to see which one matches the inverse function. The correct answer choice that matches x = 3^y is (3) y = 3^(x), since it represents the inverse relationship between x and y.

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What is the inverse of the function y=log_(3)x ?
(1) y=x^(3)
(2) y=log_(x)3
(3) y=3^(x)
(4) x=3^(y)

What is the inverse of the function $y=\log _{3} x$ ? $\newline$ (A) $y=x^{3}$ $\newline$ (B) $y=\log _{x} 3$ $\newline$ (C) $y=3^{x}$ $\newline$ (D) $x=3^{y}$

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Algebra 2

Quotient property of logarithms

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Q. What is the inverse of the function

y=\log _{3} x

\newline

(A)

y=x^{3}

\newline

(B)

y=\log _{x} 3

\newline

(C)

y=3^{x}

\newline

(D)

x=3^{y}

Identify Function Components: Identify the original function and its components. $\newline$ The original function is $y = \log_{3}(x)$ , which means that $3$ raised to the power of $y$ equals $x$ .
Write in Exponential Form: Write the original function in exponential form. $\newline$ To find the inverse, we switch $x$ and $y$ and solve for the new $y$ . So, we rewrite the equation as $x = 3^y$ .
Solve for Inverse Function: Solve for the new $y$ to express the inverse function. $\newline$ To express the inverse function, we solve for $y$ , which gives us $y = \log_{3}(x)$ . Since we have switched $x$ and $y$ , the inverse function is $x = 3^{y}$ .
Check Answer Choices: Check the answer choices to see which one matches the inverse function. $\newline$ The correct answer choice that matches $x = 3^y$ is ( $3$ ) $y = 3^{(x)}$ , since it represents the inverse relationship between $x$ and $y$ .