Answer
$log_{10}\frac{4a}{\sqrt[3] (a+1)}$
Work Step by Step
Use logarithmic properties $ln(pq) = lnp+lnq$,
$ln(\frac{p}{q}) = lnp-lnq$ and $ln(p)^{m}= m lnp$.
$log_{10}4+log_{10}a-\frac{1}{3}log_{10}(a+1)=log_{10}(4a)-log_{10}(a+1)^{\frac{1}{3}}$
This implies
$log_{10}4+log_{10}a-\frac{1}{3}log_{10}(a+1)=log_{10}\frac{4a}{\sqrt[3] (a+1)}$
