<s>[INST] Show that $19^{31}>13^{33}$ 
How can i prove that $19^{31}>13^{33}$?

What I tried
$$\bigg(\frac{19}{13}\bigg)^2=\frac{361}{169}>2>1$$
then $19^{2}>13^{2}$ and $\displaystyle 19^{30}>13^{30}$
How do I show it. Help me please. 
 [/INST] $19^{30}=(19^3)^{10}=6859^{10}\gt 13^{30}=(13^3)^{10}=2197^{10}$
$6859\gt 3\times 2197=6591$
$6859^{10}\gt (3\times 2197)^{10}=3^{10}\times 2197^{10}=3^3\times 3^3\times 3^3\times 3\times 2197^{10}=27^3\times 3\times 2197^{10}$
$27^3\times 3\times 2197^{10}\gt 13^3\times 2197^{10}$ already without even multiplying by $19.$
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