Can the output of a log be a negative, real number?

Question

In other words, is it possible that y = log (x), where x is any real or complex number yields a negative real number y as a result?

I don't think so. But I'm not a mathematician.

Stupid me. What I meant is if a logarithmic foci can be negative.

Answer 1

Most definitely.

Try log 0.1.

That's equivalent to:

10^x = 0.1

0.1 = 1/10 = 10^-1, so x = -1.

It is true, however, that you cannot take the log of a negative number, nor can you take the log of 0.

This makes sense, because, to what power could you raise 10 in order to get 0? You can't, right? Likewise, to what power could you raise 10 in order to get -1? Also impossible.

Answer 2

Logs of positive numbers less than 1 are always negative real numbers, in any base.

Answer 3

The log of 10^x where x is any negative real number is a negative real number! In fact, it is x

Answer 4

Absolutely;

If y = log(x) {which I'm taking to mean base 10), let x = 1/10. Then

log(1/10) = log [ (10)^(-1) ]

Remember, one log property states we can remove powers inside exponents outside of the log.

log[ (10)^(-1) ] = (-1) log(10)

And remember that log(10) = 1, so

(-1) log(10) = -1(1) = -1

So

log(1/10) = -1

Answer 5

yes anything to the log of the negetive power of 10 is that negetive number example
log(10^-3) = -3

Answer 6

Yes. Because the log is an exponential function .

Answer 7

all numbers <1
Try it on a calculator.