Question

Se log3 (x-y)=5 e log5 (x+y)=3, então log2 (3x-8y) é igual a?

Answer 1

$log_3(x-y)=5 \Rightarrow x-y=3^5=243\\\\log_5(x+y)=3\Rightarrow x+y=5^3=125\\\\Adicionando-se \ as \ duas \ equacoes:\\\\2x=368 \Rightarrow x=184\\\\Logo: \ y=125-184=-59\\\\log_2(3\times 184-(8\times (-59))=log_21024=10$