Question

Se log a= X e log b- Y, então:
a) log (a+b) = X=Y
b)log (ab) = x.y
c)log (a/b) = x/y
d)log (a²b) = 2x + y
e) log (1/a + 1/b) = 1/X +1/Y

Answer 1

$\large\boxed{\begin{array}{l}\underline{\sf Propriedades\,operat\acute orias\,dos\,\log \!artimos}\\\sf 1)~\rm\log_c(a\cdot b)=\log_ca+\log_cb\\\\\sf 2)~\rm\log_c\bigg(\dfrac{a}{b}\bigg)=\log_ca-\log_cb\\\\\sf 3)~\rm\log_ca^n=n\cdot \log_ca\end{array}}$

$\large\boxed{\begin{array}{l}\rm \log a=x~~\log b=y\\\rm \log(a^2\cdot b )=\log a^2+\log b\\\rm \log(a^2\cdot b)=2\log a+\log b\\\rm \log(a^2\cdot b)=2x+y\\\huge\boxed{\boxed{\boxed{\boxed{\rm\dagger\red{\maltese}~\blue{alternativa~d}}}}}\end{array}}$