# why log(0) not defined?

### 19 Answers

- BramblyspamLv 71 decade agoFavourite answer
Go back to the definition of a logarithm. It's the power that you raise a base to, in order to get the number you want.

10^3 = 1000, so log of 1000 = 3. (That's using base 10 logarithms, of course).

Now examine what happens as you reduce the power.

10^2 = 100

10^1 = 10

10^0 = 1

10^-1 = 0.1

10^-2 = 0.01

As for the log of zero, that would be the power that you have to raise 10 to in order to get zero. If you continue the pattern shown above, you can quickly see that the exponent would have to be negative infinity.

That's why log(0) is undefined.

- 1 decade ago
Any logarithmic statement can also be expressed as an

exponential statement and vice versa. Thus,

if

a

b = c (i.e. b raised to a)

then

log (c) to the base b = a

For example, since 2 raised to the power 3 = 8, we can say log (8) at base 2 = 3.

So if

log (0) to the base b = a

then

b raised to power a = 0

but there's no way to raise a number to any power and end up with

zero. So log(0) is undefined.

- 1 decade ago
Any logarithmic statement can also be expressed as an

exponential statement and vice versa. Thus,

if

a

b = c (i.e. b raised to a)

then

log (c) to the base b = a

For example, since 2 raised to the power 3 = 8, we can say log (8) at base 2 = 3.

So if

log (0) to the base b = a

then

b raised to power a = 0

but there's no way to raise a number to any power and end up with

zero. So log(0) is undefined.

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- 1 decade ago
let log(0)=x, then 0=10 to the power x, and it is not possible that any power of 10 is zero, so log(0) is not defined.

- 1 decade ago
log100=2

log 10=1

log 1=0

log .1=-1

log .01=-2

log.001=-3

If you follow this trend you will notice as the number you are finding the log of approaches zero the log of that number approaches negative infinity. Infinity as an answer in mathematics is understood as undefined

- Michael MLv 51 decade ago
If you look at a graph you will see it quickly approaching negative infinite.

log base 10 of 0 = x

0 = 10^x

What's x?

The more negative you go, the closer you get.

- 1 decade ago
if a number e.g.a is expessed as a power of another number,bi.e.,if a=b^n, then n is said to be the logrithm of a to base b.whereas the 0 cannot be a base,that's why log(0) cannot be defined.

- Anonymous1 decade ago
Because log x tends to infinity as x approaches 0. Infinities are bad things to deal with in mathematics. Same story on dividing by 0.