why can't you take the logarithm of a negative number?

Question

The definition of the log function (y = logb N, where b>0,
b not 1) is based on the definition of the exponential function

Answer 1

because logarithm is the inverse function of an exponencial function.
and the exponential function is NEVER negative

Answer 2

This Site Might Help You.

RE:
why can't you take the logarithm of a negative number?
The definition of the log function (y = logb N, where b>0,
b not 1) is based on the definition of the exponential function

Answer 3

To evaluate log(b)N, you have to find out what number must you take b to to get N. In other words, find h such that b^h = N. If N is negative, and b > 1, then there is no such real number, since positive powers are greater than 1 and negative ones are between 0 and 1, but not including 0.

There is a logarithm involving complex or imaginary numbers, but this logarithm is not unique, and in your application you are probably interested in real numbers.

Answer 4

Logarithms are short cuts to representing huge numbers. So instead of writing 1000 you write 10^3 and refer to the power ( in this case 3) as the logarithm of 1000. So let us use the following sequence:
10^3 = 10 X 10 X 10 X 1. (Write 10 3 three times and multiply it by 1 - just to make it interesting)
10 ^2 = 10 X 10 X1 (write 10 two times) So Log of 100 is 2
10^1 = 10 X 1 (write 10 one time so log of 10 is 1) So log of 10 is 1
10^0 = 1 (Write 10 zero times and multiply by 1 which is also same as DO NOT write 10 and multiply by 1)
At this point remember you CANNOT do better than writing 10 zero times and this is the boundary. So log of 1 is zero.

So Log of zero is what. I cannot determine how many times I should write 10 or even what I should write and multiply by one. So I can can safely conclude log of zero is indetminate.

Answer 5

logarithms undo exponents right?

so you cannot raise any positive number by an exponent that will change its sign.

in other words...y = logb N directly implies that b^y = N.

so, if b>0 for example 2...what number y could you use as an exponent to cause N to be negative? You can't, it's impossible, and that is why you have the definition.

Answer 6

logarithm can't take a negative number because of the anti-logarithm can be the same or below zero.

Answer 7

This happens because e^(ix)=cos(x)+i*sin(x), which can be proved by power series. In particular, e^(i*pi)=-1. You do have to be careful, though, because ln(x) is periodic in the complex numbers with period 2*pi*i, so the logarithm is not uniquely defined. This causes some of the usual rules of logs to fail.

Answer 8

Because negative log doesn't exist.

Answer 9

a = log b if b= e^a
assuming we are taking to base e

now for all real a b is > 0
so b cannot be < 0
this is true for any other base also
so we cannot take log of -ve

Answer 10

You can.
You just have to go into the realm of complex numbers to do it.