ln(y-b)=x-a

Solution for ln(y-b)=x-a equation:

Simplifying
ln(y + -1b) = x + -1a

Reorder the terms:
ln(-1b + y) = x + -1a
(-1b * ln + y * ln) = x + -1a
(-1bln + lny) = x + -1a

Reorder the terms:
-1bln + lny = -1a + x

Solving
-1bln + lny = -1a + x

Solving for variable 'b'.

Move all terms containing b to the left, all other terms to the right.

Add '-1lny' to each side of the equation.
-1bln + lny + -1lny = -1a + -1lny + x

Combine like terms: lny + -1lny = 0
-1bln + 0 = -1a + -1lny + x
-1bln = -1a + -1lny + x

Divide each side by '-1ln'.
b = al-1n-1 + y + -1l-1n-1x

Simplifying
b = al-1n-1 + y + -1l-1n-1x

Reorder the terms:
b = al-1n-1 + -1l-1n-1x + y