Quote:
For roots of positive real numbers a, and real values of k, everything is fine  you've got a realvalued logarithm, defined by an integral.

Can you explain how in
\( 64^3 = e^{3log(64)} \)
the realvalued logarithm is defined by an integral and what the integral is?
or rather
\( 64^{1/2} = e^{(1/2)log(64)} \) ? ( as you said roots).