Question

Show that $(1.01{)}^{1000}>1000$.

Answer 1

Lets take log on both sides, since the values $1.01$ & $1000$ are greater than 1 the inequality remains same.

$⟹\log {1.01}^{1000}>\log 1000$

$⟹1000\times \log 1.01>3$

$⟹1000\times 0.0043>3$

$⟹4.3>3$

Which is true and therefore we can say that $(1.01{)}^{1000}>1000$