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Answer:

This is not a reasonable solution. The negative coefficient in the exponent on the left side of the equation is not considered.

explaination:

To determine the reasonableness of the solution $x=0$ for the equation $-2^{-3x}=-2^{2x}$, we need to consider the properties of exponential equations. The equation can be rewritten as $-rac{1}{2^{3x}}=rac{1}{2^{2x}}$. The bases of the exponents are both negative, which means that the equation involves negative numbers raised to powers. In general, when dealing with exponential equations, it is important to consider the domain of the exponential function. For real numbers, the base of an exponential function cannot be negative if the exponent is not an integer. In this case, the negative coefficient in the exponent on the left side of the equation is not considered, as it violates the domain of the exponential function. Therefore, the solution $x=0$ is not a reasonable solution.

Topic: Exponential Equations and Their Properties

Tags: exponential equations mathematics reasonableness of solutions graphing functions

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Consider the equation $-2^{-3 x}=-2^{2 x}$. Which statement describes the reasonableness of the solution $x=0$?

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