Natural Log of −1
Logarithm Calculator
What is ln(−1)?
Answer
ln(−1)
does not exist
ln is the natural log, base e ≈ 2.71828.
e raised to any power is a positive number, so the negative number −1 cannot be reached.
We look for y with ey = −1.
The curve y = ln x passes through (1, 0) and (e, 1) and rises: for x > 1 the log is positive, for 0 < x < 1 negative.
The graph exists only to the right of the y-axis: there is no point at x = −1.
| Base | Notation | Value |
|---|---|---|
| e | ln(−1) | does not exist |
| 10 | log(−1) | does not exist |
| 2 | log₂(−1) | does not exist |
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Natural log of nearby numbers
| x | ln x |
|---|---|
| −5 | does not exist |
| −2 | does not exist |
| −1 | does not exist |
| 0 | does not exist |
| 0.01 | ≈ −4.6052 |
| 0.1 | ≈ −2.3026 |
| 0.2 | ≈ −1.6094 |