Ln(x-1)+ln(x+3)=ln(5)

Solution for Ln(x-1)+ln(x+3)=ln(5) equation:

Simplifying
Ln(x + -1) + ln(x + 3) = ln(5)

Reorder the terms:
nL(-1 + x) + ln(x + 3) = ln(5)
(-1 * nL + x * nL) + ln(x + 3) = ln(5)
(-1nL + nxL) + ln(x + 3) = ln(5)

Reorder the terms:
-1nL + nxL + ln(3 + x) = ln(5)
-1nL + nxL + (3 * ln + x * ln) = ln(5)
-1nL + nxL + (3ln + lnx) = ln(5)

Reorder the terms:
3ln + lnx + -1nL + nxL = ln(5)

Reorder the terms for easier multiplication:
3ln + lnx + -1nL + nxL = 5ln

Solving
3ln + lnx + -1nL + nxL = 5ln

Solving for variable 'l'.

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

Add '-5ln' to each side of the equation.
3ln + lnx + -1nL + -5ln + nxL = 5ln + -5ln

Reorder the terms:
3ln + -5ln + lnx + -1nL + nxL = 5ln + -5ln

Combine like terms: 3ln + -5ln = -2ln
-2ln + lnx + -1nL + nxL = 5ln + -5ln

Combine like terms: 5ln + -5ln = 0
-2ln + lnx + -1nL + nxL = 0

Add 'nL' to each side of the equation.
-2ln + lnx + -1nL + nL + nxL = 0 + nL

Combine like terms: -1nL + nL = 0
-2ln + lnx + 0 + nxL = 0 + nL
-2ln + lnx + nxL = 0 + nL
Remove the zero:
-2ln + lnx + nxL = nL

Add '-1nxL' to each side of the equation.
-2ln + lnx + nxL + -1nxL = nL + -1nxL

Combine like terms: nxL + -1nxL = 0
-2ln + lnx + 0 = nL + -1nxL
-2ln + lnx = nL + -1nxL

Reorder the terms:
-2ln + lnx + -1nL + nxL = nL + -1nL + -1nxL + nxL

Combine like terms: nL + -1nL = 0
-2ln + lnx + -1nL + nxL = 0 + -1nxL + nxL
-2ln + lnx + -1nL + nxL = -1nxL + nxL

Combine like terms: -1nxL + nxL = 0
-2ln + lnx + -1nL + nxL = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(-2l + lx + -1L + xL) = 0

Subproblem 1
Set the factor 'n' equal to zero and attempt to solve:

Simplifying
n = 0

Solving
n = 0

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

Add '-1n' to each side of the equation.
n + -1n = 0 + -1n
Remove the zero:
0 = -1n

Simplifying
0 = -1n

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(-2l + lx + -1L + xL)' equal to zero and attempt to solve:

Simplifying
-2l + lx + -1L + xL = 0

Reorder the terms:
-1L + -2l + lx + xL = 0

Solving
-1L + -2l + lx + xL = 0

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

Add 'L' to each side of the equation.
-1L + -2l + lx + L + xL = 0 + L

Reorder the terms:
-1L + L + -2l + lx + xL = 0 + L

Combine like terms: -1L + L = 0
0 + -2l + lx + xL = 0 + L
-2l + lx + xL = 0 + L
Remove the zero:
-2l + lx + xL = L

Add '-1xL' to each side of the equation.
-2l + lx + xL + -1xL = L + -1xL

Combine like terms: xL + -1xL = 0
-2l + lx + 0 = L + -1xL
-2l + lx = L + -1xL

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.