Логарифм помогите пожалуйста . Created by palaga61. algebra-ru

Логарифм помогите пожалуйста ...

palaga61 @palaga61

July 2022 1 9 Report

Логарифм помогите пожалуйста

Answers & Comments

mishsvyat

Ответ:

Объяснение:

Проведем преобразования в показатели степени, воспользовавшись следующими свойствами логарифма.

$1) \, log_a\,b^n=n\cdot log_a\,b\\\\2) \, log_{a^p}\,b=\frac{1}{p} \cdot log_a\,b\\\\3) \, log_a\,b+log_a\,c=log_a\,(b\cdot c)\\\\4) \, a^{log_a\,b}=b$

Тогда:

$6\cdot log_6\, \sqrt{2}=log_6 \, (\sqrt{2})^6= log_6 \, 2^3=log_6\, 8\\\\\frac{1}{3}\cdot log_6\,27= \frac{1}{3}\cdot log_6\,3^3=\frac{1}{3}\cdot 3\cdot log_6\,3=log_6\, 3\\\\\\6\cdot log_6\, \sqrt{2}+\frac{1}{3}\cdot log_6\,27=log_6\,8+log_6\,3=log_6\,(8\cdot3)=log_6\, 24$

Итоговое выражение:

$6^{\,6\cdot log_6\, \sqrt{2}+\frac{1}{3}\cdot log_6\,27}=6^{\,log_6\,8+log_6\,3}=6^{\,log_6\,(8\cdot3)}=6^{\,log_6\, 24}=24$

2 votes Thanks 1

palaga61 спасибо большое ❤️

wtbqbtbywttv помогите пожалуйста с этим заданием! https://znanija.com/task/39734080?utm_source=android&utm_medium=share&utm_campaign=question

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