I'm attempting to figure out how the equation works for the scores of hospitals in the US News & World Report 2018-2019.$^\dagger$ Specifically, I'm having trouble with the log transformation formula that they're giving on page 38-40.
Transformation is applied to the weighted reputation data using the formula $\log(R_X + 10) – 1$, where $R_X$ is the weighted reputation score for hospital X.
I'm assuming $\log$ refers to the natural logarithm, although I tried that, and a logarithm with base 10 and that didn't work either.
The article claims that:
An untransformed score of 1% has a transformed value of 4 (4 times greater)
An untransformed score of 10% has a transformed value of 29 (2.9 times greater),
An untransformed score of 60% has a transformed value of 81 (1.35 times greater)
But I've tried $\log(60+10)-1$ and that doesn't equal 81. I'm not sure where I'm going wrong.