The value of logo and log(-5) are
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I assume that “log” means the logarithm with base e, the so-called “natural logarithm”, usually abbreviated by “ ln ”.
We are looking for a value x so that ex=−5 .
Now ,−5=5⋅(−1) , and we know that 5=eln(5) (by definition of ln ),
and −1=ei⋅π , by Euler’s famous equation.
So
ex=eln(5)⋅ei⋅π=eln(5)+i⋅π
and therefore
x=ln(5)+i⋅π
This is the principal value; other values are obtained by remembering that
−1=ei∗π=ei∗(2k+1)⋅π
for any integer k .
Step-by-step explanation:
Hope it will help you. Have a great day Bro.
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