How to calculate the error bars on a log base 2 scale

Question

I have (x,y) data with with some error bars in y (represented by dy). I can log transform the data in y using

$z = \log_{10}y$

For log base 10, the error bars can be log transformed using

$dz = 0.434 \times {dy \over y}$

where dy = the error and this is explained well in this document.

My question is what should the dz equation be for log base 2 transform of y and dy? Is there an established way to log transform the error bars when plotting on a $log_{2}y$ scale?

Please forgive any mistakes in posting, it is my first time posting to Mathematics @ StackExchange. Any help is appreciated.

Answer 1

All logarithms are related by scaling: $$\log_ax=\frac{\log_bx}{\log_ba}$$ The constant $0.434$ is, more exactly, $\log_{10}e$. This means that for base 2, the constant should be $\log_2e\approx1.4427$, all else unchanged.