You cannot take a logarithm for a negative number. why do you suppose this is true?

Step-by-step explanation:

Think about it for a second.

Take log 3 (-9). 3 to what power is -9.

Let's try:

3 ^ 2 = 9. So it's not negative 9.

Maybe 3 ^ -2 = 1/9. Still not -9.

Let's try 3 ^ 1/3 = 1.4422. Still not remotely close.

So we can make a conclusion that a positive number to any real exponent can't give us a negative number.