Найти x .............. Created by llucifercute. algebra-ru

Найти x...

MizoriesKun

$1)log_{6}x=3log_{6}2+0,5log_{6}25-2log_{6}3\\ log_{6}x=log_{6}2^{3}+log_{6}25^{0,5}-log_{6}3^{2}\\ log_{6}x=log_{6}8+log_{6}5-log_{6}9\\log_{6}=log_{6}\frac{8*5}{9}\\ log_{6}x=log_{6}4\frac{4}{9}\\x=4\frac{4}{9}$

$2)lgx=\frac{1}{2}lg5a-3lgb+4lgc\\lgx=lg(5a)^{\frac{1}{2} }-lgb^{3}+lgc^{4}\\lgx=lg\sqrt{5a}-lgb^{3}+lgc^{4}\\lgx=lg\frac{\sqrt{5a}*c^{4}}{b^{3} }\\x=\frac{c^{4}*\sqrt{5a}}{b^{3} }$

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Verified answer

㏒₆x=3㏒₆2+0,5㏒₆25-2㏒₆3

㏒₆x=㏒₆2³+ ㏒₆√25- ㏒₆3²

㏒₆x=㏒₆8+ ㏒₆5- ㏒₆9

㏒₆x=㏒₆ 8*5/9

х=40/9

lgx=1/2lg5a -3lg b +4lg c

lgx=lg√5a -lg b³ +lg c⁴

lgx=lg √(5a)*c⁴/b³

x= √(5a)*c⁴/b³

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