TITLE: anyone can help me with solving this $x^{x^{3}}=3$?
QUESTION [6 upvotes]: Find the value of $x$ : $x^{x^{3}}=3$
I tied with "log" but I couldn't. any help?

REPLY [8 votes]: A nice first step toward the solution is to increase the symmetry of the LHS: if you cube $x^{x^3}$, you get $x^{3x^3}$, which is $(x^3)^{x^3}$.  Symmetry!  Since cubing the RHS gives $3^3$, it's easy to then spot the solution $x^3=3$.