How do you take a log of a negative number? For example, what is the answer for Log -1? Log -0.08? Log -1.5?
Can you please show me the steps that need to be taken in order to take a log of a negative number, and what mathematical theory (IE: base formula of a log, etc) you used in order to get the value of a negative logarithm? Thanks
It can be, but the solution would be in Complex. That's what I am wondering.
Thanks. So, if I follow this form, let's say I am calculating log(-4):
Therefore,
log(-4) = log4 + i/pi
log(-4) (approximately)= 0.602 + i/pi
Is this the way to calculate it? What would the value of i/pi be here? My calculator states that it would be approximately 1.36i, but I don't understand how it managed to multiply (sqrt) -1 by 3.14
I am just wondering in general. Whenever I take a log of a negative number, the answer is always in the form of:
log (-x) = log(x) + 1.364376i.
How is the latter term (1.364376i) obtained? I have done multiplying i by pi, but that just gives me 3.14i. Do you know (or anyone else know) a site where I can see the proof of a logarithm with a negative arguement? Thanks again.
The basic definition followed by the change of base rule since seems to use a lot
which is where the pi part comes from
When b=10 you get and
^ EDIT III: changed log(10) to ln(10) as it should be ln
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EDIT: I'll try to test by solving
As then we get
Remembering to divide by ln(10) gives
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EDIT II: The basic formula is . I would suggest using the change of base rule to put into the form first where is a constant
I used google as my calculator and the inspiratation came from How to find the log of a negative number? - Yahoo! UK & Ireland Answers