Question

Sa se rezolve in multime numerelor reale ecuatia $log_{2} x+ log_{4} x +log_{8} x=11/6$

Answer 1

$log_{2}x + log_{2^{2}}x + log_{2^{3}}x = \frac{11}{6}$

$log_{2}x + \frac{1}{2}log_{2}x + \frac{1}{3}log_{2}x = \frac{11}{6}$

$log_{2}x ( 1+ 1/2 + 1/3 ) = 11/6$

$\frac{11}{6}* log_{2}x = \frac{11}{6}$

$log_{2}x = 1 => x = 2$