tex] с решением пжл)) ...

Yhanna @Yhanna

July 2022 1 15 Report

Вычислите:

а)[tex]2log_{\sqrt{5}}25+\frac{1}{3}log_{2}64[/tex]

б)[tex]4log_{6}216-2log_{0,5}(log_{3}81)[/tex]

в)[tex]2log_{2}\frac{1}{4}+3log_{\frac{1}{3}}27[/tex]

г)[tex]5logx_{\frac{1}{5}}625+81log_{4}(log_{16}256)[/tex]

с решением пжл))

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dtnth

Verified answer

$2log_{ \sqrt{5} } 25 + 1/3log_2 64=2log_{5^{1/2}} } 5^2 + 1/3log_2 2^6=2*2*2+1/3*6=6+2=8;$

$4log_{6}216-2log_{0,5}(log_{3}81)=4log_{6} 6^3 - 2log_{0,5}(log_{3} 3^4)= 4*3 - 2log_{0,5} 4=12 - 2log_{0,5} 0.5^{-2}=12-2*(-2)=12+4=16;$

$2log_{2}\frac{1}{4}+3log_{\frac{1}{3}}27=2log_{2}\ 2^{-2}+3log_{\frac{1}{3}} \frac{1}{3}^{-3}= =2*(-2)+3*(-3)=-4-9=-13;$

$5logx_{\frac{1}{5}}625+81log_{4}(log_{16}256) =5logx_{\frac{1}{5}} \frac{1}{5})^{-4}+81log_{4}(log_{16} 16^2)=5*(-4)+81*log_{4} 2=-20+81*log_{2^2} 2=-20+81/2=-20+40.5=20.5$

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