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

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

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

Multiply nL * x
nxL + ln(x + -1) = ln(x + 4)

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

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

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

Add '-1lnx' to each side of the equation.
-1ln + lnx + -1lnx + nxL = 4ln + lnx + -1lnx

Combine like terms: lnx + -1lnx = 0
-1ln + 0 + nxL = 4ln + lnx + -1lnx
-1ln + nxL = 4ln + lnx + -1lnx

Combine like terms: lnx + -1lnx = 0
-1ln + nxL = 4ln + 0
-1ln + nxL = 4ln

Solving
-1ln + nxL = 4ln

Solving for variable 'l'.

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

Add '-4ln' to each side of the equation.
-1ln + -4ln + nxL = 4ln + -4ln

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

Combine like terms: 4ln + -4ln = 0
-5ln + nxL = 0

Add '-1nxL' to each side of the equation.
-5ln + nxL + -1nxL = 0 + -1nxL

Combine like terms: nxL + -1nxL = 0
-5ln + 0 = 0 + -1nxL
-5ln = 0 + -1nxL
Remove the zero:
-5ln = -1nxL

Divide each side by '-5n'.
l = 0.2xL

Simplifying
l = 0.2xL