In(0) is -infinity. (check explanation below)

Technically, In(0) is undefined! but,

What is the logarithm of a number to a base?

The (loga base b) ask us what power would we raise b to get a. That is, (log8 base 2) ask us what power would we raise 2 to get 8 which is 3 because 2^3=8.

where ln is the way to indicate the natural log or log in base e . But how do you find the right b value such that ...

Now to what is ln(0)?

We know that lnx = logx base e (where e is approx 2.71828).

ln(0) ask us what power would we raise e to get 0?

e^-(infinity) is approx. 0 (because, e^-(infinity) = 1/e^(infinity) = 1/infinity ~= 0)

Ans: In(0) = -infinity

ln (1) | 0 |
---|---|

ln (2) | 0.693147 |

ln (3) | 1.098612 |

ln (4) | 1.386294 |

ln (5) | 1.609438 |