Question

Determine os valores de x para que exista:

a) logx 10

b) log10(x − 3)

c) log½(−x² + 5x − 4)
alguém me ajuda por favor ​

Answer 1

$\boxed{\begin{array}{l}\tt a)~\sf\ell og_x10\\\sf 1\ne x>0\\\tt b)~\sf\ell og_{10}(x-3)\\\sf x-3>0\\\sf x>3\\\tt c)~\sf\ell og_{\frac{1}{2}}-x^2+5x-4\\\sf -x^2+5x-4>0\\\sf g(x)=-x^2+5x-4\\\sf g(x)=0\\\sf -x^2+5x-4=0\\\sf\Delta=25-16=9\\\sf x=\dfrac{-5\pm3}{-2}\begin{cases}\sf x_1=1\\\sf x_2=4\end{cases}\\\sf g(x)>0\Longleftrightarrow 1<x<4\end{array}}$