Question

Seja f : R*+ -> R uma função definida por f(x) = log (x) na base b. Sabendo-se que f(b) = c-2 e f(b/c) = -1 , o valor de (b + c) é:

Answer 1

$\large\boxed{\begin{array}{l}\rm f(x)=\log (x)\\\rm f(b)=\log(b)\\\rm \log (b)=c-2\\\rm b=10^{c-2}\\\rm f\bigg(\dfrac{b}{c}\bigg)=\log\bigg(\dfrac{b}{c}\bigg)\\\\\rm \log\bigg(\dfrac{b}{c}\bigg)=-1\\\\\rm\dfrac{b}{c}=10^{-1}\\\\\rm\dfrac{b}{c}=\dfrac{1}{10}\longrightarrow c=10b\\\\\rm b+c=b+10b=11b\end{array}}$