Evaluate natural log of 7e^4

Problem

ln(7*e4)

Solution

1. Identify the expression as a natural logarithm of a product, which allows the use of the product rule for logarithms: ln(a*b)=ln(a)+ln(b)

2. Apply the product rule to separate the constant 7 and the exponential term e4

ln(7*e4)=ln(7)+ln(e4)

3. Apply the power rule for logarithms, ln(xk)=k*ln(x) to the second term.

ln(7)+ln(e4)=ln(7)+4*ln(e)

4. Simplify the expression using the property that the natural log of the base e is 1 so ln(e)=1

ln(7)+4*(1)=ln(7)+4

Final Answer

ln(7*e4)=ln(7)+4

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