# why log(0) not defined?

Relevance

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.

• Anonymous
4 years ago

Log Of 0

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.

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.

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.

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

let log(0)=x

10^x=0

there is no x such that 10^x =0

so not defined

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.