Ln(2x+7)=ln(x-4)

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Solution for Ln(2x+7)=ln(x-4) equation: 


Simplifying
Ln(2x + 7) = ln(x + -4)

Reorder the terms:
nL(7 + 2x) = ln(x + -4)
(7 * nL + 2x * nL) = ln(x + -4)
(7nL + 2nxL) = ln(x + -4)

Reorder the terms:
7nL + 2nxL = ln(-4 + x)
7nL + 2nxL = (-4 * ln + x * ln)
7nL + 2nxL = (-4ln + lnx)

Solving
7nL + 2nxL = -4ln + lnx

Solving for variable 'n'.

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

Add '4ln' to each side of the equation.
7nL + 4ln + 2nxL = -4ln + 4ln + lnx

Reorder the terms:
4ln + 7nL + 2nxL = -4ln + 4ln + lnx

Combine like terms: -4ln + 4ln = 0
4ln + 7nL + 2nxL = 0 + lnx
4ln + 7nL + 2nxL = lnx

Add '-1lnx' to each side of the equation.
4ln + 7nL + -1lnx + 2nxL = lnx + -1lnx

Reorder the terms:
4ln + -1lnx + 7nL + 2nxL = lnx + -1lnx

Combine like terms: lnx + -1lnx = 0
4ln + -1lnx + 7nL + 2nxL = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(4l + -1lx + 7L + 2xL) = 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 '(4l + -1lx + 7L + 2xL)' equal to zero and attempt to solve:

Simplifying
4l + -1lx + 7L + 2xL = 0

Reorder the terms:
7L + 4l + -1lx + 2xL = 0

Solving
7L + 4l + -1lx + 2xL = 0

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

Add '-7L' to each side of the equation.
7L + 4l + -1lx + -7L + 2xL = 0 + -7L

Reorder the terms:
7L + -7L + 4l + -1lx + 2xL = 0 + -7L

Combine like terms: 7L + -7L = 0
0 + 4l + -1lx + 2xL = 0 + -7L
4l + -1lx + 2xL = 0 + -7L
Remove the zero:
4l + -1lx + 2xL = -7L

Add '-4l' to each side of the equation.
4l + -1lx + -4l + 2xL = -7L + -4l

Reorder the terms:
4l + -4l + -1lx + 2xL = -7L + -4l

Combine like terms: 4l + -4l = 0
0 + -1lx + 2xL = -7L + -4l
-1lx + 2xL = -7L + -4l

Add 'lx' to each side of the equation.
-1lx + lx + 2xL = -7L + -4l + lx

Combine like terms: -1lx + lx = 0
0 + 2xL = -7L + -4l + lx
2xL = -7L + -4l + lx

Add '-2xL' to each side of the equation.
2xL + -2xL = -7L + -4l + lx + -2xL

Combine like terms: 2xL + -2xL = 0
0 = -7L + -4l + lx + -2xL

Simplifying
0 = -7L + -4l + lx + -2xL

The solution to this equation could not be determined.

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

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