What is the value of log -2?

Answer 1

[ln(2) + i*pi]/ln(10) if you are referring to log as a base 10 log. ln refers to the

natural logarithm (log base e)

The log of any negative number is imaginary. The formula above is derived from

the relationship:

-1 = ei*pi

since you want log of -2, multiply both sides by 2

-2 = 2*ei*pi

taking natural logarithm of both sides: ln( -2) = ln(2*ei*pi ) = ln(2) + ln(ei*pi )

which reduces to ln(2) + i*pi

If you want log10 then divide both sides by ln(10)

So log10(-2) = ln(-2)/ln(10) = [[ln(2) + i*pi]/ln(10)
x = log (-2) = log10(-2)

10x = -2

Think about the smallest possible number you can put in for x.

10-∞ = ?

10-∞ = 1/10∞

10∞ = ∞

1/∞ = ?

1/∞ = 0

It is impossible to ever get 0 or a negative number because you will never reach infinity.

log(-2) is undefined