Question

Se log5 x=2 e log5 y=3, determine log5 (x.y) e log xy

Answer 1

$\boxed{\begin{array}{l}\underline{\sf Logaritmo\,do\,produto}\\\sf \log_c(a\cdot b)=\log_ca+\log_cb\\\sf \log_5x=2\implies x=5^2\\\sf \log_5y=3\implies y=5^3\\\sf \log_5(x\cdot y)=\log_5x+\log_5y=2+3=5\\\\\sf \log(xy)=\log(5^2\cdot 5^3)=\log(5^5)=5\log5=3,49 \end{array}}$