I think I figured it out.

Transformations of f(x)=log₁₀(x) -> f(x)=2log₁₀(x-4)+3

Vertical stretch: f(x)=log₁₀(x) -> f(x)=2log₁₀x

Horizontal translation: f(x)=2log₁₀x -> f(x)=2log₁₀(x-4)

Vertical translation: f(x)=2log₁₀(x-4) -> f(x)=2log₁₀(x-4)+3

In terms of x and y, the vertical stretch and vertical translation would affect y, and the horizontal translation would affect x. Therefore, it would be (x+4, 2y+3).

This can be checked by using the point (1, 0) on :

(1+4, 2(0)+3)

= (5, 3)

(5, 3) is a point on the graph f(x)=2log₁₀(x-4)+3.