Question

simplify e^ln4

Answer 1

By the definition of the natural logarithm, \[e^{\ln x} = x\]because the log of a number is just the value that the base needs to be raised to to give the number. The base of the natural logarithm is \(e\).

It's maybe easier to see with base 10 logs. \(\log_{10} 1000 = 3\) because \(10^3 = 10*10*10 = 1000\)
That means that \[10^{\log_{10} 1000} = 10^3 = 1000\]demonstrating that raising the base to the log of a number gives you the number.

Answer 2

ok thank you! i got the answer i needed!