Which one is larger: $$37^{38}\quad\text{or}\quad38^{37}$$
I solved it as follow:
First I divided both numbers by $37^{37}$ to get $37$ and $(\frac{38}{37})^{37}$. Since $(1+\frac1{37})^{37}<e<37$ We have $$37^{38}>38^{37}$$ I'm looking for other approaches. Can you please solve it differently?