How to apply one of the laws of logarithms to rearrange an equation? I want to rearrange the logarithm of a ratio shown in the paper here for figure 3 < It is shown as `log10(corneal diameter/ axial length) = -0.22` But I want to get it in terms of axial length. Appendix 1 of this paper does just this < and says: `axial length = corneal diameter * 10^-0.22` However, I've been criticised for using this and that it should be: `axial length=corneal Diameter/10^-0.22` So I turned to wolfram alpha and inputted: log10(x/y)=-z, solve for y which gave: y = x * 10^0.22 equivalent to: axial length = corneal diameter * 10^0.22 So I have three different answers to what should be a trivial rearrangement. Much appreciated if you can tell me who's correct. Thanks. Apologies if the links aren't accessible to all but I've tried to replicate everything in full here.

The last two answers are correct and hence are the same. Your equation is $$\mathrm{log}_{10}\frac{d}{L} = a$$ $$\frac{d}{L} = 10^{a}$$ $$L = \frac{d}{10^{a}} = \frac{d}{10^{-0.22}} = d\,10^{0.22}$$ We let $a=-0.22$, $d=$ corneal diameter, and $L=$ axial length.