Find the Domain 20*(6000 natural log of e^(2.5t))

Problem

20*(6000*ln(e(2.5*t)))

Solution

1. Identify the components of the expression that could restrict the domain. The expression contains a natural logarithm function ln(u) and an exponential function eu

2. Analyze the natural logarithm. The function ln(u) is defined only when its argument u is strictly greater than zero (u>0.

3. Evaluate the argument of the logarithm. In this expression, the argument is e(2.5*t)

4. Determine the range of the exponential function. For any real number t the value of e(2.5*t) is always strictly positive (e(2.5*t)>0.

5. Conclude the domain. Since e(2.5*t) is always positive for all real values of t there are no values of t that make the expression undefined.

Final Answer

Domain=(−∞,∞)

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