Question

2log3 ^2(x)-7log3(x)+3=0​

Answer 1

$2log_3(x)^2-7log_3(x)+3=0\\\\\\ODZ:\ \ x>0\\\\\\log_3(x)=t\\\\\\2t^2-7t+3=0\\\\\\D=49-24=25=5^2\\\\\\t_1=\dfrac{7-5}{4}=\dfrac{2}{4}=\dfrac{1}{2}\\\\\\t_2=\dfrac{7+5}{4}=\dfrac{12}{4}=3\\\\\\t_1=\dfrac{1}{2}\qquad\ \ \ \ \ \ \ \ t_2=3\\\\\\log_3(x)=\dfrac{1}{2}\qquad\log_3(x)=3\\\\\\x_1=3^{\frac{1}{2}}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x=_13^3\\\\\\x_1=\sqrt3\ \ \ \ \ \ \ \ \ \ \ \ x_2=27 \ \ \ \ , \ \ \ \ x_{1,2}>0$