Question

O valor do logaritmo log(base4) 2(raiz quadrada)2?

Answer 1

$log_{4}2 \sqrt{2} = x$
Usando a propriedade do logaritmo:
$4^{x}=2 \sqrt{2}$
$4^{x}= 2^{1} . 2^{ \frac{1}{2} }$
$4^{x} = 2 ^{ \frac{3}{2} }$
$(2^{2}) ^{x} = 2 ^{\frac{3}{2}$
$2 ^{2x} = 2 ^{\frac{3}{2} }$
$2x = \frac{3}{2}$
$x = \frac{3}{2} . \frac{1}{2} = \frac{3}{4} = 0,75$