Find the Domain 2^(3y-2)=3^(2y+5)

Problem

2^(3*y−2)=3^(2*y+5)

Solution

1. Identify the type of equation provided. This is an exponential equation where the variable y is in the exponents.

2. Analyze the functions involved. Exponential functions of the form a^ƒ(y) are defined for all real numbers as long as the base a is positive and the exponent ƒ(y) is defined.

3. Determine the constraints on the exponents. The exponents 3*y−2 and 2*y+5 are linear polynomials, which are defined for all real values of y

4. Conclude the domain. Since there are no denominators, square roots of negative numbers, or logarithms of non-positive numbers, there are no restrictions on y

Final Answer

Domain=(−∞,∞)

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