2⋅log3 0,1+log3 8100.. Created by melodywhite. algebra-ru

2⋅log3 0,1+log3 8100...

melodywhite @melodywhite

July 2022 1 28 Report

2⋅log3 0,1+log3 8100.

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lilyatomach

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Ответ:

Объяснение:

Воспользуемся следующими свойствами логарифма

Для некоторого числа р и чисел

$a>0, a\neq 1;\\b>0,c>0$

выполняются равенства

$log{_a}b +log{_a}c =log{_a}(b\cdot c);\\log{_a}b ^{p} =p\cdot log{_a}b;\\log{_a}a=1.$

$2\cdot log{_3}0,1+log{_3}8100= log{_3}0,1^{2} +log{_3}8100= log{_3}0,01+log{_3}8100=\\\\= log{_3}(0,01\cdot 8100)= log{_3}81= log{_3}3^{4} = 4\cdot log{_3}3=4\cdot1=4$

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