Ln(x+4)=ln(2x+1)

Solution for Ln(x+4)=ln(2x+1) equation:

Simplifying
Ln(x + 4) = ln(2x + 1)

Reorder the terms:
nL(4 + x) = ln(2x + 1)
(4 * nL + x * nL) = ln(2x + 1)
(4nL + nxL) = ln(2x + 1)

Reorder the terms:
4nL + nxL = ln(1 + 2x)
4nL + nxL = (1 * ln + 2x * ln)
4nL + nxL = (1ln + 2lnx)

Solving
4nL + nxL = 1ln + 2lnx

Solving for variable 'n'.

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

Add '-1ln' to each side of the equation.
4nL + -1ln + nxL = 1ln + -1ln + 2lnx

Reorder the terms:
-1ln + 4nL + nxL = 1ln + -1ln + 2lnx

Combine like terms: 1ln + -1ln = 0
-1ln + 4nL + nxL = 0 + 2lnx
-1ln + 4nL + nxL = 2lnx

Add '-2lnx' to each side of the equation.
-1ln + 4nL + -2lnx + nxL = 2lnx + -2lnx

Reorder the terms:
-1ln + -2lnx + 4nL + nxL = 2lnx + -2lnx

Combine like terms: 2lnx + -2lnx = 0
-1ln + -2lnx + 4nL + nxL = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(-1l + -2lx + 4L + 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 n to the left, all other terms to the right.

Simplifying
n = 0
Subproblem 2
Set the factor '(-1l + -2lx + 4L + xL)' equal to zero and attempt to solve:

Simplifying
-1l + -2lx + 4L + xL = 0

Reorder the terms:
4L + -1l + -2lx + xL = 0

Solving
4L + -1l + -2lx + xL = 0

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

Add '-4L' to each side of the equation.
4L + -1l + -2lx + -4L + xL = 0 + -4L

Reorder the terms:
4L + -4L + -1l + -2lx + xL = 0 + -4L

Combine like terms: 4L + -4L = 0
0 + -1l + -2lx + xL = 0 + -4L
-1l + -2lx + xL = 0 + -4L
Remove the zero:
-1l + -2lx + xL = -4L

Add 'l' to each side of the equation.
-1l + -2lx + l + xL = -4L + l

Reorder the terms:
-1l + l + -2lx + xL = -4L + l

Combine like terms: -1l + l = 0
0 + -2lx + xL = -4L + l
-2lx + xL = -4L + l

Add '2lx' to each side of the equation.
-2lx + 2lx + xL = -4L + l + 2lx

Combine like terms: -2lx + 2lx = 0
0 + xL = -4L + l + 2lx
xL = -4L + l + 2lx

Add '-1xL' to each side of the equation.
xL + -1xL = -4L + l + 2lx + -1xL

Combine like terms: xL + -1xL = 0
0 = -4L + l + 2lx + -1xL

Simplifying
0 = -4L + l + 2lx + -1xL

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
n = {0}