Question

The value of log0 and log(-5) are​

Answer 1

Answer:

Answer

Updated January 25

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 .

Answer 2

Answer:

log 0 is undefined. it's not a real number because you can never get zero by raising anything to the power of anything else.