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**Negative**Number

**ln**(x) is definedonly for x>0. So the natural logarithm of a

**negative**number is undefined. The complex logarithmic function Log(z) isdefined for

**negative**numbers too.

Correspondingly, why can't you ln a negative number?

If **you** raise a **negative number** to apositive **number** that's not an integer, but instead afraction or a decimal, **you** might end up with a **negativenumber** underneath a square root. So in summary, because thebase can only be a positive **number**, that means the argumentof the logarithm can only be a positive **number**.

Rule name | Rule |
---|---|

ln of negative number | ln(x) is undefined when x ≤ 0 |

ln of zero | ln(0) is undefined |

ln of one | ln(1) = 0 |

ln of infinity | lim ln(x) = ∞ ,when x→∞ |

Additionally, what does negative log mean?

**Negative** Logarithms A **negative logarithm means** how many times todivide by the number. We can have just one divide: Example: What is**log**_{8}(0.125) ? Well, 1 ÷ 8 = 0.125, So**log**_{8}(0.125) = −1.

The real natural logarithm function **ln**(x) isdefined only for x>**0**. So the natural logarithm of zero isundefined.