Find the Domain 100^2+100^2=100^x

Problem

100+100=100

Solution

1. Identify the type of equation. This is an exponential equation where we are looking for the domain of the variable x that satisfies the equality.

2. Simplify the left side of the equation by combining like terms.

100+100=2⋅100

3. Rewrite the equation using the simplified left side.

2⋅100=100

4. Determine the domain. In an exponential equation of the form ab=cx where a>0 the variable x can be any real number for the expression 100 to be defined.

5. Analyze the specific solution for x to ensure it exists. By taking the logarithm of both sides, we find x=(log_100)(2⋅100) which is a well-defined real number.

6. Conclude that since there are no square roots of negative numbers, denominators that could be zero, or logarithms of non-positive numbers involving the variable x in the original expression, the domain is all real numbers.

Final Answer

Domain:x∈ℝ

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