As per exponential equation, the value of 'y' in terms of 'x' is [tex]log_{3}(\frac{4}{x})[/tex].
What is an equation?
"An equation combines two expressions connected by an equal sign. These two expressions on either side of the equals sign are called the “left-hand side” and “right-hand side” of the equation.
We generally assume the right-hand side of an equation is zero. This will not reduce the generality since we can balance this by subtracting the right-hand side expression from both sides’ expressions."
What is an exponential equation?
"Exponential equations, as the name suggests, involve exponents. We know that the exponent of a number (base) indicates the number of times the number (base) is multiplied.
When the power is a variable and if it is a part of an equation, then it is called an exponential equation. We may need to use the connection between the exponents and logarithms to solve the exponential equations."
Given, [tex]x = 4(3)^{-y}[/tex]
⇒ [tex]\frac{x}{4} = (3)^{-y}[/tex]
⇒ [tex]log(\frac{x}{4})= log (3^{-y})[/tex]
⇒ [tex]log (\frac{x}{4}) = -y[log (3)][/tex]
⇒ [tex]y = \frac{log (\frac{4}{x})}{log(3)}[/tex]
⇒ [tex]y = log_{3}(\frac{4}{x})[/tex]
Hence,
As per exponential equation, the value of 'y' in terms of 'x' is [tex]log_{3}(\frac{4}{x})[/tex].
Learn more about an exponential equation here: https://brainly.com/question/26540624
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