ln(x+1)-in(x+3)=ln(x-4)

Solution for ln(x+1)-in(x+3)=ln(x-4) equation:

Simplifying
ln(x + 1) + -1in(x + 3) = ln(x + -4)

Reorder the terms:
ln(1 + x) + -1in(x + 3) = ln(x + -4)
(1 * ln + x * ln) + -1in(x + 3) = ln(x + -4)
(1ln + lnx) + -1in(x + 3) = ln(x + -4)

Reorder the terms:
1ln + lnx + -1in(3 + x) = ln(x + -4)
1ln + lnx + (3 * -1in + x * -1in) = ln(x + -4)
1ln + lnx + (-3in + -1inx) = ln(x + -4)

Reorder the terms:
-3in + -1inx + 1ln + lnx = ln(x + -4)

Reorder the terms:
-3in + -1inx + 1ln + lnx = ln(-4 + x)
-3in + -1inx + 1ln + lnx = (-4 * ln + x * ln)
-3in + -1inx + 1ln + lnx = (-4ln + lnx)

Add '-1lnx' to each side of the equation.
-3in + -1inx + 1ln + lnx + -1lnx = -4ln + lnx + -1lnx

Combine like terms: lnx + -1lnx = 0
-3in + -1inx + 1ln + 0 = -4ln + lnx + -1lnx
-3in + -1inx + 1ln = -4ln + lnx + -1lnx

Combine like terms: lnx + -1lnx = 0
-3in + -1inx + 1ln = -4ln + 0
-3in + -1inx + 1ln = -4ln

Solving
-3in + -1inx + 1ln = -4ln

Solving for variable 'i'.

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

Add '-1ln' to each side of the equation.
-3in + -1inx + 1ln + -1ln = -4ln + -1ln

Combine like terms: 1ln + -1ln = 0
-3in + -1inx + 0 = -4ln + -1ln
-3in + -1inx = -4ln + -1ln

Combine like terms: -4ln + -1ln = -5ln
-3in + -1inx = -5ln

Combine like terms: -5ln + 5ln = 0
-3in + -1inx + 5ln = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(-3i + -1ix + 5l) = 0

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

Simplifying
n = 0

Solving
n = 0

Move all terms containing i 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 '(-3i + -1ix + 5l)' equal to zero and attempt to solve:

Simplifying
-3i + -1ix + 5l = 0

Solving
-3i + -1ix + 5l = 0

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

Add '-5l' to each side of the equation.
-3i + -1ix + 5l + -5l = 0 + -5l

Combine like terms: 5l + -5l = 0
-3i + -1ix + 0 = 0 + -5l
-3i + -1ix = 0 + -5l
Remove the zero:
-3i + -1ix = -5l

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.