Can the Anti-log of a Number Be Negative?

[Yashbhatt]

If we accept both positive and negative values for the square root of a number, then can the anti-log of a number be negative?

 

[Simon Bridge]

You should be able to work that out from the definition of the logarithm (and what "antilogarithm" means.)http://en.wikipedia.org/wiki/Logarithm#Inverse_function

if $y=b^x$ then $\log_b(y)=x$

$\text{antilog}_b x (= b^x) = y$

You want to know if y can be negative.

Presumably your concern is that the log is not defined for negative values of y.
It is a bit like the surd for square roots ... to account for negative values, define: $\log_b|y|=x$, i.e. take the absolute value. Then there are two possible values going the other way.
Otherwise you are implicitly requiring a positive value for y as the original input.

 

[Yashbhatt]

So, is it like we have both positive and negative values but we keep only positive values?

 

[Simon Bridge]

Like that - which values we use depends on the context.
Maybe we will need both of them.

BTW: it is possible to have a negative base ... that can give a negative or a complex antilog.