Which is greater : $66^{70}$ or $70^{66}?$
My approach:
Consider $x^y > y^x$. This is true if and only if $\ln x^y > \ln y^x$, $y \ln x > x \ln y$ $\frac{\ln x}{\ln y} > \frac{x}{y}$. Therefore $66^{70} > 70^{66}$, since $\frac{\ln 66}{\ln 70} \approx 0.98615027281$ and $\frac{66}{70} = \frac{33}{35} \approx 0.942857142857$
But this solution is based on Logarithmic table.Is there any rigorous method?
Any help would be highly appreciated!
Thank you!
