Why is the log of a negative number not defined, Learn How to find logarithm of negative numbers
Why is the log of a negative number not defined? Or Why is log not defined for negative values? Or Can you evaluate a log for a negative number?
All of these questions have the same meaning. So, the best way to get the answer to these questions is to put a negative input in log and see what happens?
Suppose y equals log-base-10 of negative 3; which can be written as the natural log of negative 3 upon a natural log of 10.
Since negative three equals the product of negative one and three; we can write a natural log of negative three equals, the sum of the natural log of negative one and the natural log of three.
Now, we can write a negative one equals the sum of the cosine of pi and iota times sine of pi.
I am ignoring general form, here.
By using Euler's formula, we can write a negative one equals “e” to the “i PI.
Taking the natural log on both sides of this equation, we get a natural log of negative one equals “I" times PI.
Which is a purely imaginary number.
If we substitute the value of the natural log of negative one, we get y equals the sum of iPi and the natural log of 3 upon a natural log of 10.
This implies; y is an imaginary number, which is often called a complex number.
When we talk about complex functions, it is fine. But in case of real-valued-functions; negative input is not defined at all.
So, what next? If really want to know why can’t the base of a log be negative, then watch this.
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