Find the Domain 3^(x+1)+3^(x-2)-3^(x-3)+3^(x-4)=750

Problem

3^(x+1)+3^(x−2)−3^(x−3)+3^(x−4)=750

Solution

1. Identify the type of equation. This is an exponential equation where the variable x appears in the exponents of terms with a constant base of 3

2. Recall the definition of the domain for exponential functions. An exponential function of the form a^ƒ(x) is defined for all values of x for which the exponent ƒ(x) is defined.

3. Analyze the exponents. The exponents in this equation are x+1 x−2 x−3 and x−4

4. Determine the constraints. Each of these exponents is a linear polynomial. Polynomials are defined for all real numbers.

5. Conclude that there are no values of x that would result in an undefined expression (such as division by zero or taking the square root of a negative number) within the exponents.

Final Answer

Domain=(−∞,∞)

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