Why can't the base of a logarithm be negative?

Asked Feb 25 '14 at 21:08

Active Feb 25 '14 at 21:08

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I understand why the base of a logarithm can't be 0 or 1, but why negative?

What I found out is that when the base is negative we get imaginary results when the powers are rational numbers with odd denominators, for example:

$$-2^{\frac{1}{2}}$$

is undefined, thus the logarithm is not defined either?

Is this true? and if it's, is that the only reason? Thanks.

asked Feb 25 '14 at 21:08

Mahmoud Ahmed

Actually, the example you posted is defined, because it is the square root of 2 with a negative up front – imranfat Feb 25 '14 at 21:16
Do you mean it's equivalent to $-1 * \sqrt{2}$? – Mahmoud Ahmed Feb 25 '14 at 21:17
I would put parentheses around the $(-2)$. – mr eyeglasses Feb 25 '14 at 21:24
OP already asked essentially the same question here – MJD Feb 25 '14 at 21:24
Really didn't get that part :) – Mahmoud Ahmed Feb 25 '14 at 21:26
@MJD, Note that your link starts https: which causes Latex not to render correctly. – Peter Phipps Feb 25 '14 at 21:36

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