Is it possible to find the log of a negative number

It is possible to evaluate one, however, the answer will be a complex number. We will use the change-of-base rule and convert to natural logarithms, to make things easier later:. We can exploit the addition property of logarithms, and separate this part into two separate logs:.

Now the only problem is figuring out what ln -1 is. It might look like an impossible thing to evaluate at first, but there is a pretty famous equation known as Euler's Identity that can help us. This result comes from power series expansions of sine and cosine. I won't explain that too in-depth, but if you are interested, there is a nice page here which explains a bit more. So, now that we know what ln -1 is, we can substitute back into our equation:.

Since, the base a raised to any exponent n is positive, the number b must be positive. The logarithm of a negative number b is undefined. The base of a log function is also the base of an exponential function. Since logarithms are defined for real numbers, the base of a log function must be positive. However, it is possible to determine the log of an imaginary number or a negative number using Euler's identity.

Embed Share via. Table of contents: Why do we need to learn about logarithms? What is a logarithm? How to calculate negative logarithms? An example of negative log calculation FAQ. Why do we need to learn about logarithms? Do you know how many 2's you have to multiply together to get 8? Before going any further, let should first try to understand what a logarithm is!

An example of negative log calculation To demonstrate how to find the negative log of any number using our online negative log calculator , let us calculate the value of -log 2 8 : Enter the number you want to calculate the negative logarithm of, i. Enter the base, i. If you want to calculate the natural log, use e as the base. The negative log value, i. FAQ Can log be negative? That was But it works and if you study complex analysis it will be derived in great detail.

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