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.

 

[CellCoree]

The anti-log of a number cannot be negative. The anti-log function, also known as the inverse logarithmic function, is used to find the original value from a given logarithmic value. The logarithmic function itself is only defined for positive numbers, so the anti-log function can only produce positive values.

It is important to note that the square root and logarithmic functions are different from the anti-log function. While the square root function can produce both positive and negative values, the logarithmic function only produces positive values. Therefore, the argument of accepting both positive and negative values for the square root of a number does not apply to the anti-log function.

In summary, the anti-log of a number cannot be negative, as it is only defined for positive values and is used to find the original value from a logarithmic value.