Question

Show that ${\left(\frac{21}{20}\right)}^{100}$ is greater than $100$.

Answer 1

Let $x={\left(\frac{21}{20}\right)}^{100}$

Taking $\log$ on both sides, we get

$\log x=100(\log 21-\log 20)=100(\log 3+\log 7-\log 2-1)$

$\Rightarrow \log x=132.22193-130.10300=2.11893>2$

$\Rightarrow \log x>\log 100⟹x>100$