Ok, got it. To change from log-log to lin-lin one can do:
y₂ = MathConstants.e .^ ( a .* log.(x) .+ b .* log.(10))
I did use WolframAlpha, I fed it log10(y) = a * log10(x) + b
It says the answer is approximate form. I then changed it to Julia form.
log₁₀y == a * log₁₀x + b
10 ^ log₁₀y == 10 ^ ( a * log₁₀x + b )
y == 10 ^ ( a * log₁₀x + b )
y == 10 ^ ( a * log₁₀x ) * 10 ^ b
magic..
y == MathConstants.e .^ ( a .* log.(x) .+ b .* log.(10))
Above is pseudo-code.