Question

$\frac{1}{\frac{1}{2}-log(x)}$ = y. Simplificar a equação, se possível de forma bem explicada.

Answer 1

$\displaystyle \text y = \frac{1}{\frac{1}{2}-\text{Log(x)}} \\\\\\ \text y = \frac{1}{\frac{\displaystyle 1-2\text{Log(x)}}{2}} \\\\\\ \text y = 1.\frac{2}{1-2\text{Log(x)}} \\\\\\ \text y = \frac{2}{1-\text{Log(x)}^2 }$

mas sabemos que Log 10 = 1, então podemos escrever assim :

$\displaystyle \text y = \frac{2}{\text{Log 10}-\text{Log(x)}^2 }$

Usando a propriedade, sabemos também que :

$\displaystyle \text{Log a} - \text{Log b } = \text{Log}\ (\frac{\text a}{\text b} )$

Então, vamos reescrever o denominador assim :

$\displaystyle \text y = \frac{2}{\displaystyle \text{Log}\ (\frac{10}{\text x^2}) }$

$\displaystyle \text y = 2.[\text{Log}\ (\frac{10}{\text x^2}) ]^{-1} \\\\\\ \huge\boxed{\text y = 2.[\ \text{Log} \ (\frac{10}{\text x^2})\ ]^{-1} }\checkmark$