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July 2022 1 16 Report

ОТ ДУШИ, ТОВАРИЩИ, ПРОШУ.
Найти наибольшее целое значение х, удовлетворяющее условию:
[tex]-log _ \frac{1}{ \sqrt{3}} (x-5)+2log _{ \sqrt{3}}(x-5)\ \textless \ 4[/tex]

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Luluput

Verified answer

$-log _ \frac{1}{ \sqrt{3}} (x-5)+2log _{ \sqrt{3}}(x-5)\ \textless \ 4$
ОДЗ:
$x-5\ \textgreater \ 0$
$x\ \textgreater \ 5$

$log _ \sqrt{3}} (x-5)+2log _{ \sqrt{3}}(x-5)\ \textless \ 4$
$3log _{ \sqrt{3}}(x-5)\ \textless \ 4$
$log _{ \sqrt{3}}(x-5)^3\ \textless \ log _{ \sqrt{3}}( \sqrt{3} )^4$
$(x-5)^3\ \textless \ ( \sqrt{3} )^4$
$(x-5)^3\ \textless \ 9$
$(x-5)^3\ \textless \ (\sqrt[3]{9})^3$
$x-5\ \textless \ \sqrt[3]{9}$
$x\ \textless \ \sqrt[3]{9}+5$

-----------(5)-------------------(5+∛9)----------------
////////////////////////

$x$ ∈ $(5;$ $5+ \sqrt[3]{9} )$

$\sqrt[3]{8} \ \textless \ \sqrt[3]{9} \ \textless \ \sqrt[3]{27}$
$2\ \textless \ \sqrt[3]{9} \ \textless \ 3$
$7\ \textless \ \sqrt[3]{9}+5 \ \textless \ 8$

наибольшее целое решение: 7

Ответ: 7

3 votes Thanks 2

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