Are fractional exponents considered logarithms? Say I have a number with a fractional exponent, $10^{\frac{1}{3}}$. Could this number be considered a logarithm, even though it is not written as $10^{0.\overline{3}}$?

The question "What is $\log_bx$?" is equivalent to "What power do I need to raise $b$ to in order to get $x$?"
The question "What is $\sqrt[n]{x}$ ($=x^{\frac1n}$)?" is equivalent to "What number should I raise to the power $n$ in order to get $x$?"
They are both questions about an equation of the form $a^b=c$. That being said, I wouldn't call $10^\frac13$ a logarithm.
