I'll try to proceed stp-by-step.
We convert the log-log graph into a linear one by this change of variables:
x = log10(I[lux])
y = log10(R[kΩ])
Then we have the same graph but the abscissa axis is linear (ranging from -1 to 5) and the y too (ranging from -1 to 3).
It is a straight line whose equation is
(y-2)/x = (y+1)/(x-4)
It simplifies to
x = -4/3 * (y+1) + 4
Then, reaplacing and grouping terms, etc...:
log10(I[lux]) = -4/3 * ( log10(R[kΩ])+1 ) + log10(10000)
log10(I[lux]) = log10(R[kΩ]*10)^(-4/3) + log10(10000)
log10(I[lux]) = log10 [ (R[kΩ]*10)^(-4/3) * 10000 ]
I[lux]) = (R[kΩ]*10)^(-4/3) * (10000)
I[lux] = 10000 / (R[kΩ]*10)^(4/3)
Regards
Z