The order of which time complexity is higher, 3 ^ log(n) or n ^ 3? Which one has a higher order time complexity:


$n ^ 3$
$3 ^ {\log n}$


I know that an exponential time order is higher than polynomials. However, it uses a logarithmic power which is low for a large n, while n^3 or more could remain still high, not?
The answer easily follows from the identity $3^{\log n} = n^{\log 3}$. Whether or not $\log 3 &lt; 3$ depends on the basis of the logarithm.