what is the natural logarithm of ( -0.2877 ) which is a negative number?

Answer 1

This one has multiple values, expressed by the formula:

k = -1.24584... + (2n+1) π

where n is any integer, so that e^k = -0.2877

Answer 2

The short answer: there's no solution for real numbers. This is asking "e to what power gives you -0.2877?". You can't take the log of a negative number, regardless of the base, because a number raised to any power (which is what the log is in reverse) is always a positive number.

The long answer: There are strange ways of expressing the value in with complex numbers if you really wanted to. First, factor out the -1:

Ln(-0.2877) = Ln(-1 * 0.2877) = Ln (-1) + Ln(0.2877)

Euler's formula says e^(ix)=cosx+isinx, which for x=pi gives you e^(i*pi) = -1. This also means Ln(-1) = (i*pi). So you could express the answer is i*pi + Ln(0.2877).

Answer 3

It is not defined. In fact the logarithms of any negative number is not defined. Its kinda like 1/0.

Natural log of 1 is,
ln1 = 0

Its because exp (0) is 1.

But we can find no real number whose exp value is a negative number.



SO , exp ( something) can never be negative whatever that something may be.

ln (-0.2877) is that something. But that something can never exist.

However a complex number may exist.

Answer 4

e^(pi*i) = -1

Multiply this famous fact by 0.2877 and take the logarithm of both sides. You get pi * i * ln (0.2877); work the rest out with your calculator

Answer 5

Negative numbers DO NOT HAVE logarithm

Answer 6

According to Google Calculator, it's -1.24583701 + 3.14159265 i

Answer 7

I got -1.245637008 + (Pi)*i
i = sqrt(-1)

so -1.245637008 + pi * sqrt(-1)

Answer 8

1/ln(.2877)