Write the quantity using sums and differences of simpler logarithmic expressions. Express your answer so that logarithms of products, quotient and powers do not appear.
@nycmath, This may be the last reply I shall ever give you.
Frankly I am fed-up with your posting a raw question, but with your showing no effort whatsoever.
$\log \left[ {\sqrt[3]{{x\sqrt {1 + {y^2}} }}} \right] = \frac{1}{3}\left[ {\log (x) + \frac{1}{2}\log \left( {1 + {y^2}} \right)} \right]$