Question

Se a>0 , b>0, b≠1 e log (a+b)=log a + log b, então o
valor de a é?

Answer 1

Olá, Cristiano.

$\log (a+b)=\log a + \log b\Rightarrow\\\\ \log (a+b)=\log (a\cdot b)\Rightarrow\\\\ a+b=ab\Rightarrow\\\\ a-ab=-b\Rightarrow\\\\ a(1-b)=-b\Rightarrow\\\\a=\frac{-b}{1-b}\Rightarrow\\\\\boxed{a=\frac{b}{b-1}}$