Find the Domain 4^x+32=12*2^x

Problem

4+32=12⋅2

Solution

1. Identify the type of equation. This is an exponential equation where the variable x appears in the exponents of terms with bases 4 and 2

2. Analyze the expressions for restrictions. Exponential functions of the form ax (where a>0 are defined for all real numbers.

3. Check for denominators or roots. There are no fractions with variables in the denominator and no even-indexed roots (like square roots) that would restrict the input values.

4. Determine the domain. Since there are no operations that result in undefined values for any real number x the domain consists of all real numbers.

Final Answer

Domain=(−∞,∞)

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