Log of 0 (Base 10)

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What is log 0?

Answer

log 0

does not exist

log here is the common log, base 10.

10 raised to any power is greater than zero, so no power gives 0. The closer x gets to 0, the lower log x: log 0.001 = −3.

We look for y with 10^y = 0.

The curve y = log x passes through (1, 0) and (10, 1) and rises: for x > 1 the log is positive, for 0 < x < 1 negative.

The graph has no point at x = 0: the curve goes down along the y-axis.

log 0 does not exist

It decreases without bound (to −∞): log 0.001 = −3, log 0.0001 = −4. There is no value at x = 0 itself.

e ≈ 2.71828 is the base of the natural logarithm: ln x is the logarithm of x to base e, so ln e = 1. It is an irrational number, like π.