Can also write
a = log(4/3) → log4 - log3 → log(2^2) - log3 → 2log2 - log3
and
b = log(10/9) → log10 - log9 → 1 - log(3^2) → 1 - 2log3. (I'm assuming log is log to base 10)
From these you should be able to rearrange to get log2 and log3 in terms of a and b.