Some coloring algorithms gives an upper bound for the locating chromatic number of trees with all the vertices not in an end-path colored by only two colors. That means, a better coloring algorithm could be achieved by optimizing the number of colors used in the end-paths. We provide an estimation of the locating chromatic number of trees using the locating chromatic number of its end-palms. We also study the locating chromatic number of palms, a subdivision of star. We also prove $χ_L(S_n(k))=Θ(n^{1/k})$; $χ_L(S_n(3))=(1+o(1))\sqrt[3]{4n}$; and $χ_L(O_n)=\left\lceil\log_3\left(\frac{n}{4}\right)\right\rceil+3$.