СРОЧНО РЕШИТЕ УРАВНЕНИЕ ПЖЛ eogосн3*(2-x)-1=logосн3*5+logосн3*(x+4). Created by Triton3000. algebra-ru

СРОЧНО РЕШИТЕ УРАВНЕНИЕ ПЖЛ eogосн3*(2-x)-1=logосн3*5+logосн3*(x+4)...

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July 2022 1 4 Report

СРОЧНО РЕШИТЕ УРАВНЕНИЕ ПЖЛ
eogосн3*(2-x)-1=logосн3*5+logосн3*(x+4)

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$log_3(2-x)-1=log_35+log_3(x+4)\\\\ODZ:\; \left \{ {{2-x\ \textgreater \ 0} \atop {x+4\ \textgreater \ 0}} \right. \; \left \{ {{x\ \textless \ 2} \atop {x\ \textgreater \ -4}} \right. \; \; \Rightarrow \; \; -4\ \textless \ x\ \textless \ 2\\\\log_3(2-x)-log_33=log_35(x+4)\\\\log_3 \frac{2-x}{3} =log_3(5x+20)\\\\ \frac{2-x}{3} =5x+20\\\\2-x=15x+60\\\\16x=-58\\\\x=-\frac{58}{16}\\\\x=-3,625\in ODZ$

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