Предмет: Алгебра, автор: Ilyasssssss

Сравните числа $a= 5^{200} , b= 2^{500}$

Ответы

Автор ответа: Алкадиеныч

Прологарифмируем числа 5^200 и 2^500
$lg 5^{200} and, lg 2^{500} 2lg5 and, 5lg2 lg25 and,lg32$
$lg25\ \textless \ lg32$
Значит
5^200<2^500

Автор ответа: skvrttt

$5^{200}~and~2^{500}\\25^{100}~and~32^{100}\\25\ \textless \ 32\to25^{100}\ \textless \ 32^{100}$

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