Find the Domain natural log of e^(5x)

Problem

ln(e(5*x))

Solution

1. Identify the function as ƒ(x)=ln(e(5*x))

2. Recall the domain requirements for a natural logarithm function ln(u) which is that the argument u must be strictly greater than zero (u>0.

3. Set up the inequality for the argument of the logarithm: e(5*x)>0

4. Analyze the exponential function eu Since e is a positive constant (≈2.718, any power of e is always positive for all real values of u

5. Conclude that e(5*x)>0 is true for all real numbers x

Final Answer

Domain of *ln(e(5*x))=(−∞,∞)

Want more problems? Check here!