równanie logarytmiczne

[enigma]

\(\displaystyle{ log_{3}(3\cdot x) log_{3}x = log_{3}9}\)

[wb]

\(\displaystyle{ log_{3}(3\cdot x) log_{3}x = log_{3}9 \\(log_3 3+log_3 x)log_3 x=2 \\ log_3^2 x+log_3 x-2=0 \\ log_3 x=t \\ t^2+t-2=0 \\ t=-2 t=1 \\ log_3 x=-2\vee log_3x= 1 \\ x=3^{-2}\vee x=3^1}\)