negative value in log_b(x) inside the parameter b

[shahar]

In the expression:

Why b cannot be negative number?

 

[Dr.Peterson]

In the expression:
View attachment 34495
Why b cannot be negative number?

What thoughts do you have?

If b were negative, how would the function be defined? Can you see any harm in that?

The best answer to "why is it this way?" is often "try it and see". You can learn a lot that way. Have you tried?

 

[shahar]

O.K. I remember that was a reason of trying but I don't see it now.
I saw it in the past but "coin" don't drop to me.
I think the reason is there is no (square) root to negative number. But I don't know if I am right....

 

[topsquark]

O.K. I remember that was a reason of trying but I don't see it now.
I saw it in the past but "coin" don't drop to me.
I think the reason is there is no (square) root to negative number. But I don't know if I am right....

[imath]x = log_b(a) \Leftrightarrow a = b^x[/imath]

So, if we have b = -4, can we do [imath]x = log_{-4} (2) \Leftrightarrow 2 = (-4)^x[/imath]?

-Dan

 

[Steven G]

What would be the sign of a negative number raised to ____?
You fill in the blank with some numbers. Another hint: There are numbers other than integers and rational numbers.

 

[shahar]

What would be the sign of a negative number raised to ____?
You fill in the blank with some numbers. Another hint: There are numbers other than integers and rational numbers.

complex?

 

[Steven G]

complex?

No. try some real numbers.