I am currently preparing for a interview that is notorious for asking mental approximations. Two example questions came up: 1) $\ln 514$ and 2) $3^{3.6}$.

What are some of the best ways to calculate these on the spot? For 1), my consideration was to use the change of base $\ln 514 = \log_2 514/\log_2 e \approx \log_2 512/0.7 = 90/7$, but even that seems like a bit of a stretch. For 2), my approach was to use $3^{3.6}>3^3\sqrt{3}\approx 27\times 1.7$, which once again seems like a stretch.

Does anyone have better/more efficient/creative ways of approximating these? Please share, thank you!