Đáp án:
$\text{a) $2^{300}$ < $3^{200}$.}$
$\text{b) $3^{24}$ > $64^{3}$.}$
$\text{c) $5^{7}$ > $25^{3}$.}$
Giải thích các bước giải:
$\text{a) Ta có:}$
`2^300=(2^3)^100=8^100.`
`3^200=(3^2)^100=9^100.`
$\text{Vì $8^{100}$ < $9^{100}$ nên $2^{300}$ < $3^{200}$}$
$\text{Vậy $2^{300}$ < $3^{200}$.}$
$\text{b) Ta có:}$
`3^24=(3^8)^3=6561^3.`
$\text{Vì $6561^{3}$ > $64^{3}$ nên $3^{24}$ > $64^{3}$}$
$\text{Vậy $3^{24}$ > $64^{3}$.}$
$\text{c) Ta có:}$
`25^3=(5^2)^3=5^6.`
$\text{Vì $5^{7}$ > $5^{6}$ nên $5^{7}$ > $25^{3}$}$
$\text{Vậy $5^{7}$ > $25^{3}$.}$
