Trying to simplify a logarithmic exponent

Question

I am solving a recurrence and ended up with n^(lgk/lgn), where lg is in base 2. Can we simplify n^(lgk/lgn) even further? I really cannot see it !!

Thank you.

Answer 1

Since \begin{align*} \frac{\log_b(x)}{\log_b(y)}=\log_y(x) \end{align*}

we get \begin{align*} n^{\frac{\log_2(k)}{\log_2(n)}}=n^{\log_n(k)}=k \end{align*}