Помогите решить . Не понимаю Log(осн.2)24-1/2Log(осн.2)72. Created by oivanovml2008. algebra-ru

2Log(осн.2)72...

oivanovml2008 @oivanovml2008

September 2021 2 16 Report

Помогите решить . Не понимаю
Log(осн.2)24-1/2Log(осн.2)72

Nananey2000 Vashe zadanie resheno

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Kixcertborn2 Verno

Kixcertborn2

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$log_2(24)- \frac{1}{2} log_2(72)=log_2(6*2^2)-\frac{1}{2}log_2(6^2*2)= \\ \\ =log_2(6*2^2)-log_2( \sqrt{6^2*2} )=log_2(6*2^2)-log_2( 6\sqrt{2} )= \\ \\ 
=log_2( \frac{6*2^2}{6\sqrt{2}} )=log_2( \frac{(\sqrt{2})^4}{\sqrt{2}} )=log_2((\sqrt{2})^3)=log_2(2^{ \frac{3}{2}} )= \frac{3}{2} log_2(2)=1.5$

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