Решите логарифмы: [50 баллов] :). Created by topwkolnik. algebra-ru

Решите логарифмы: [50 баллов] :)...

topwkolnik @topwkolnik

August 2022 1 11 Report

Решите логарифмы: [50 баллов] :)

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m11m

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А)
$1) log_{0.4}( \frac{1}{5}* \sqrt[3]{50} )=log_{ \frac{2}{5} } \sqrt[3]{ \frac{50}{125} }=log_{ \frac{2}{5} } \sqrt[3]{ \frac{2}{5} }= log_{ \frac{2}{5} }( \frac{2}{5} )^{ \frac{1}{3} }= \frac{1}{3}$

$2) log_{0.6}( \frac{ \sqrt{15} }{5} )=log_{ \frac{3}{5} } \frac{ \sqrt{15} }{ \sqrt{25} }=log_{ \frac{3}{5} }( \frac{3}{5} )^{ \frac{1}{2} }= \frac{1}{2}$

$3) log_{0.32}( \frac{2 \sqrt{2} }{5} )=log_{ \frac{32}{100} } \frac{ \sqrt{8} }{ \sqrt{25} }=log_{ \frac{8}{25} }( \frac{8}{25} )^{ \frac{1}{2} }= \frac{1}{2}$

$4) \frac{1}{3}+ \frac{1}{2}+ \frac{1}{2}=1 \frac{1}{3}$

в)
$4^{ \frac{1}{2log_{625}16} }$

$1) 2log_{625}16=log_{5^4}16^2=log_{5^4}2^8= \frac{8}{4} log_{5}2=log_{5}2^2= \\ 
 \\ 
=log_{5}4= \frac{1}{log_{4}5}$

$2) 4^{ \frac{1}{ \frac{1}{log_{4}5} } }=4^{log_{4}5}=5$

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