lg^5 x - 3lg^3 x - 4 lgx = 0. Created by romana2507pc07t9. algebra-ru

lg^5 x - 3lg^3 x - 4 lgx = 0...

romana2507pc07t9 @romana2507pc07t9

July 2022 1 5 Report

lg^5 x - 3lg^3 x - 4 lgx = 0

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$lg^5x-3\, lg^3x-4\, lgx=0\; ,\; \; \; ODZ:\; x>0\\\\lgx\, (lg^4x-3\, lg^2x-4)=0\\\\a)\; \; lgx=0\; ,\; \; \underline {x=1}\\\\b)\; \; lg^4x-3lg^2x-4=0\\\\t=lg^2x\geq 0\; \to \; \; t^2-3t-4=0\; \; ,\; \; t_1=-1\; ,\; t_2=4>0,\\\\ t_1=-1$

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