log3x+3logx3=4

[monita_1990]

^log3^x+3logx³⁼⁴

[Zarrie]

[tex]log_{3}x+3log_{x}3=4[/tex]
[tex]D(x):x>0,x\neq 1[/tex]
Използваме това, че [tex]log_{x}3=\frac{1}{log_{3}x} \Rightarrow log_{3}x+\frac{3}{log_{3}x}=4[/tex]
[tex]log_{3}x=t[/tex]
[tex]t+\frac{3}{t}=4[/tex]
[tex]t^2-4t+3=0,t_{1}=1,t_{2}=3[/tex]
[tex]log_{3}x=1\Rightarrow x=3\in D(x)[/tex]
[tex]log_{3}x=3\Rightarrow x=27\in D(x)[/tex]

[monita_1990]

Много благодаря