Question

Ecuatie logaritmica:
$log_{9} (2x+10)*log_{x+1}3=1$

Answer 1

x>-1;x≠0
$log_{9}(2x+10)* log_{x+1}3=1 \\ log_{3^2}(2x+10)* \frac{1}{ log_{3}(x+1) } = 1 \\ log_{3^2}(2x+10)= log_{3}(x+1) \\ \sqrt{2x+10}=x+1 \\ 2x+10= x^{2} +2x+1 \\ x^{2} -9=0 \\ x=-3;x=3$
x=-3 nu poate fi solutie,conform conditiei de mai sus
S={3}