0
[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
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