Ln(4x-7)=ln(x+5)

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Solution for Ln(4x-7)=ln(x+5) equation: 


Simplifying
Ln(4x + -7) = ln(x + 5)

Reorder the terms:
nL(-7 + 4x) = ln(x + 5)
(-7 * nL + 4x * nL) = ln(x + 5)
(-7nL + 4nxL) = ln(x + 5)

Reorder the terms:
-7nL + 4nxL = ln(5 + x)
-7nL + 4nxL = (5 * ln + x * ln)
-7nL + 4nxL = (5ln + lnx)

Solving
-7nL + 4nxL = 5ln + lnx

Solving for variable 'n'.

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

Add '-5ln' to each side of the equation.
-7nL + -5ln + 4nxL = 5ln + -5ln + lnx

Reorder the terms:
-5ln + -7nL + 4nxL = 5ln + -5ln + lnx

Combine like terms: 5ln + -5ln = 0
-5ln + -7nL + 4nxL = 0 + lnx
-5ln + -7nL + 4nxL = lnx

Add '-1lnx' to each side of the equation.
-5ln + -7nL + -1lnx + 4nxL = lnx + -1lnx

Reorder the terms:
-5ln + -1lnx + -7nL + 4nxL = lnx + -1lnx

Combine like terms: lnx + -1lnx = 0
-5ln + -1lnx + -7nL + 4nxL = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(-5l + -1lx + -7L + 4xL) = 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 '(-5l + -1lx + -7L + 4xL)' equal to zero and attempt to solve:

Simplifying
-5l + -1lx + -7L + 4xL = 0

Reorder the terms:
-7L + -5l + -1lx + 4xL = 0

Solving
-7L + -5l + -1lx + 4xL = 0

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

Add '7L' to each side of the equation.
-7L + -5l + -1lx + 7L + 4xL = 0 + 7L

Reorder the terms:
-7L + 7L + -5l + -1lx + 4xL = 0 + 7L

Combine like terms: -7L + 7L = 0
0 + -5l + -1lx + 4xL = 0 + 7L
-5l + -1lx + 4xL = 0 + 7L
Remove the zero:
-5l + -1lx + 4xL = 7L

Add '5l' to each side of the equation.
-5l + -1lx + 5l + 4xL = 7L + 5l

Reorder the terms:
-5l + 5l + -1lx + 4xL = 7L + 5l

Combine like terms: -5l + 5l = 0
0 + -1lx + 4xL = 7L + 5l
-1lx + 4xL = 7L + 5l

Add 'lx' to each side of the equation.
-1lx + lx + 4xL = 7L + 5l + lx

Combine like terms: -1lx + lx = 0
0 + 4xL = 7L + 5l + lx
4xL = 7L + 5l + lx

Add '-4xL' to each side of the equation.
4xL + -4xL = 7L + 5l + lx + -4xL

Combine like terms: 4xL + -4xL = 0
0 = 7L + 5l + lx + -4xL

Simplifying
0 = 7L + 5l + lx + -4xL

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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