Question

Calcule o valor dos logaritmo
$log\frac{1}{4} \sqrt[2]{2}$
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Answer 1

$log(10) ( \frac{1}{4} ) \times \sqrt{2} \\ \\ log(10) ( {2}^{ - 2}) \times \sqrt{2} \\ \\ - 2 log(10) (2) \times \sqrt{2} \\ \\ s = - 2 log(10) (2) \times \sqrt{2}$

Answer 2

Resposta:

$\log_{1\over4}\sqrt{2} =x\\ \\ ({1\over4})^x=\sqrt{2} \\ \\ ({1\over2^2})^x=2^{1\over2}\\ \\ 2^{-2x}=2^{1\over2}\\ \\ -2x={1\over2}\\ \\ -4x=1\\ \\ 4x=-1\\ \\ x=-\dfrac{1}{4}$