How do you evaluate log_8 (-1/64)?

1 Answer
Bill K.
Aug 4, 2016

As stated, there is no answer since there is no real number to which 8 can be raised to give a negative number. The following equations are true, however, if you are interested: log_{8}(1/64)=-2 and log_{8}((1/64)^{-1})=2.

Explanation:

By definition, for x>0, log_{8}(x) is the unique real number satisfying the condition that 8^{log_{8}(x)}=x. Since 8^{y}>0 for all real y, the quantity log(-1/64) has no real number answer.

For the other examples given, since 8^{-2}=1/(8^2)=1/64 and 8^{2}=64, it follows that log_{8}(1/64)=-2 and log_{8}((1/64)^{-1})=2.

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