Step by step
The question
Question: solve e to the power x = −3.
x is up in the power.
ex = −3
e is a special number, like π.
It is about 2.718.
A log with base e is written ln.
We say "natural log".
e ≈ 2.718
ln = loge
1 Look at the sign
e is positive.
A positive number to any power is positive.
It is never negative.
eany power > 0
So it can never be −3.
There is no solution.
No power of e is −3.
Answer
No power of e is −3.