Anti-log of a number

  1. 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?
     
  2. jcsd
  3. Simon Bridge

    Simon Bridge 15,280
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    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.
     
  4. So, is it like we have both positive and negative values but we keep only positive values?
     
  5. Simon Bridge

    Simon Bridge 15,280
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    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.
     
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