[tex]loc_c(a^m)=mlog_ca \\log_ca+log_cb=log_c(a \times b) \\ a^x \times a^y=a^{x+y}\\ \\ 5^2=25 \\ 5^4=625 \\ \\ 5log625+25log625+625log625= \\ log(625^5)+log(625^{25})+log(625^{625})= \\ log(5^{4 \times 5}) + log(5^{4 \times 25}) + log(5^{4 \times 625}) = \\ log5^{20}+log5^{100}+log5^{2500}= \\ log(5^{20}\times5 ^{100} \times 5^{2500})= \\ log5^{20+100+2500}= \\ log5^{2620}= \\ 2620log5[/tex]
