Question

Log raiz quadrada de 2 = x na base 4 . me ajudem .?

Answer 1

$log_4 \ \sqrt{2} \ = \ x$

$log_4 \ (2)^{\frac{1}{2}} \ = \ x$

$(2)^{\frac{1}{2}} \ = \ 4^x$

$2^{\frac{1}{2}} \ = \ (2^2)^x$

$2^{\frac{1}{2}} \ = \ 2^{2x}$

Cancelando as bases:

$\not{2}^{\frac{1}{2}} \ = \ \not{2}^{2x}$

$\frac{1}{2} \ = \ 2x$

$x \ = \ \frac{\frac{1}{2}}{2}$

$x \ = \ \frac{1}{2} \ . \ \frac{1}{2}$

$\boxed{\bold{x \ = \ \frac{1}{4}}}$