Find the Domain (3.4)^(2x+3)=8.5

Problem

(3.4)(2*x+3)=8.5

Solution

1. Identify the type of equation provided. This is an exponential equation where the variable x is located in the exponent.

2. Determine the constraints for the exponential function. An exponential function of the form ƒ(x)=ag(x) is defined for all real numbers as long as the base a is a positive constant (a>0 and the exponent g(x) is defined.

3. Analyze the base and the exponent. The base 3.4 is a positive constant. The exponent 2*x+3 is a linear polynomial, which is defined for all real numbers.

4. Conclude that there are no values of x that make the expression undefined. Therefore, the domain consists of all real numbers.

Final Answer

Domain=(−∞,∞)

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