It also works for inflation or other yearly recurring charges. Those small percentages add up quickly - at 3% inflation and 2% charges the value of your investment in today's dollars/euros will halve in 14 years. Yikes!
Few people can do logarithms in their heads - and those that can, usually do it using similar tricks. I realize that "doing math in your head" is well on the decline, but it is pretty essential for speedy approximations, which are what many decisions tend to be based on.
70 / x = number of years of constant growth required for a quantity to double given that it grows at x percent
The example used in the video: if the price of lift tickets goes up by 7% per year, in 10 years, that price will double.
(and actually, the constant 70 is an approximation, the actual constant is ln (2) * 100)