ln(x-1)-ln(x+4)=5

Solution for ln(x-1)-ln(x+4)=5 equation:

Simplifying
ln(x + -1) + -1ln(x + 4) = 5

Reorder the terms:
ln(-1 + x) + -1ln(x + 4) = 5
(-1 * ln + x * ln) + -1ln(x + 4) = 5
(-1ln + lnx) + -1ln(x + 4) = 5

Reorder the terms:
-1ln + lnx + -1ln(4 + x) = 5
-1ln + lnx + (4 * -1ln + x * -1ln) = 5
-1ln + lnx + (-4ln + -1lnx) = 5

Reorder the terms:
-1ln + -4ln + lnx + -1lnx = 5

Combine like terms: -1ln + -4ln = -5ln
-5ln + lnx + -1lnx = 5

Combine like terms: lnx + -1lnx = 0
-5ln + 0 = 5
-5ln = 5

Solving
-5ln = 5

Solving for variable 'l'.

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

Divide each side by '-5n'.
l = -1n-1

Simplifying
l = -1n-1