Ln(x-4)+ln(x-1)=ln(x-8)

Solution for Ln(x-4)+ln(x-1)=ln(x-8) equation:

Simplifying
Ln(x + -4) + ln(x + -1) = ln(x + -8)

Reorder the terms:
nL(-4 + x) + ln(x + -1) = ln(x + -8)
(-4 * nL + x * nL) + ln(x + -1) = ln(x + -8)
(-4nL + nxL) + ln(x + -1) = ln(x + -8)

Reorder the terms:
-4nL + nxL + ln(-1 + x) = ln(x + -8)
-4nL + nxL + (-1 * ln + x * ln) = ln(x + -8)
-4nL + nxL + (-1ln + lnx) = ln(x + -8)

Reorder the terms:
-1ln + lnx + -4nL + nxL = ln(x + -8)

Reorder the terms:
-1ln + lnx + -4nL + nxL = ln(-8 + x)
-1ln + lnx + -4nL + nxL = (-8 * ln + x * ln)
-1ln + lnx + -4nL + nxL = (-8ln + lnx)

Add '-1lnx' to each side of the equation.
-1ln + lnx + -4nL + -1lnx + nxL = -8ln + lnx + -1lnx

Reorder the terms:
-1ln + lnx + -1lnx + -4nL + nxL = -8ln + lnx + -1lnx

Combine like terms: lnx + -1lnx = 0
-1ln + 0 + -4nL + nxL = -8ln + lnx + -1lnx
-1ln + -4nL + nxL = -8ln + lnx + -1lnx

Combine like terms: lnx + -1lnx = 0
-1ln + -4nL + nxL = -8ln + 0
-1ln + -4nL + nxL = -8ln

Solving
-1ln + -4nL + nxL = -8ln

Solving for variable 'l'.

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

Add '8ln' to each side of the equation.
-1ln + -4nL + 8ln + nxL = -8ln + 8ln

Reorder the terms:
-1ln + 8ln + -4nL + nxL = -8ln + 8ln

Combine like terms: -1ln + 8ln = 7ln
7ln + -4nL + nxL = -8ln + 8ln

Combine like terms: -8ln + 8ln = 0
7ln + -4nL + nxL = 0

Add '4nL' to each side of the equation.
7ln + -4nL + 4nL + nxL = 0 + 4nL

Combine like terms: -4nL + 4nL = 0
7ln + 0 + nxL = 0 + 4nL
7ln + nxL = 0 + 4nL
Remove the zero:
7ln + nxL = 4nL

Add '-1nxL' to each side of the equation.
7ln + nxL + -1nxL = 4nL + -1nxL

Combine like terms: nxL + -1nxL = 0
7ln + 0 = 4nL + -1nxL
7ln = 4nL + -1nxL

Divide each side by '7n'.
l = 0.5714285714L + -0.1428571429xL

Simplifying
l = 0.5714285714L + -0.1428571429xL