Произведение корней уравнения log3x×log4x=log3 4

[latex]log_3x\cdot log_4x=log_34\; ,\; \; \; \; ODZ :\; x\ \textgreater \ 0\\\\log_3x\cdot \frac{log_3x}{log_34} =log_34\qquad \; \; [\; log_{a}b= \frac{log_{c}b}{log_{c}a}\; ]\\\\ \frac{log_3^2x}{log_34} =log_34\\\\log_3^2x =log_3^24[/latex] [latex]log_3^2x-log_3^24=0\\\\(log_3x-log_34)(log_3x+log_34)=0\\\\\star \; \; log_3x=log_34\; \; \to \; \; x=4\\\\\star \; \; log_3x=-log_34\; ,\; \; x=4^{-1}\; ,\; \; x= \frac{1}{4} [/latex]