[tex]Use:\\log_ab^c=c\times log_ab\\\\log_ab+log_ac=log_a(b\times c)\\\\log_ab-log_ac=log_a(b:c)\\\\log_aa=1[/tex]
[tex]\frac{1}{3}log125-2log4+log32=log125^\frac{1}{3}-log4^2+log32\\\\=log\sqrt[3]{125}-log16+log32=log5-log16+log32\\\\=log(5:16\times32)=log\left(\frac{5}{16}\times32\right)=log(5\times2)=log10=1[/tex]
