Question

log de 2 na base x + log de x na base 16 = 5/4

Answer 1

$log_{x}2+log_{16}x= \frac{5}{4} \\ \frac{log_{2}2}{log_{2}x} + \frac{log_{2}x}{log_{2}16}= \frac{5}{4} \\ \frac{1}{log_{2}x} + \frac{log_{2}x}{4}= \frac{5}{4} \\ \frac{4}{4log_{2}x}+ \frac{(log_{2}x)^{2}}{4log_{2}x} = \frac{5}{4} \\ \frac{4+2log_{2}x}{4log_{2}x}= \frac{5}{4} \\ 4+2log_{2}x= \frac{5}{4} 4log_{2}x \\ log_{2}16+2log_{2}x=5log_{2}x \\ log_{2}16=3log_{2}x \\ log_{2}16=log_{2}x^{3} \\ x^{3}=16 \\ x= 2\sqrt[3]{2}$

Não sei se está certo.