Question

Sa se rezolve ecuatia:
$13 log{x}3 = \frac{1}{10} log_{3} x+ log_{x} 27$

Answer 1

㏒x 27=㏒x 3³=3㏒x 3
Notam ㏒x 3=t
13t=1/10*1/t+3t
13t=1/10t+3t, inmultim cu 10 t
130t²=1+30t²
100t²=1 ⇒t²=1/100 ⇒t1=1/10, t2=-1/10
㏒x 3=1/10  ⇒ 
x^{1/10}=3 ⇒x= 3^{10} 
㏒x 3=1/10  ⇒ 
x^{-1/10}=3 ⇒x= 1/3^{10}