Ln(3x-7)=ln(5-x)

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Solution for Ln(3x-7)=ln(5-x) equation: 


Simplifying
Ln(3x + -7) = ln(5 + -1x)

Reorder the terms:
nL(-7 + 3x) = ln(5 + -1x)
(-7 * nL + 3x * nL) = ln(5 + -1x)
(-7nL + 3nxL) = ln(5 + -1x)
-7nL + 3nxL = (5 * ln + -1x * ln)
-7nL + 3nxL = (5ln + -1lnx)

Solving
-7nL + 3nxL = 5ln + -1lnx

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

Reorder the terms:
-5ln + -7nL + 3nxL = 5ln + -5ln + -1lnx

Combine like terms: 5ln + -5ln = 0
-5ln + -7nL + 3nxL = 0 + -1lnx
-5ln + -7nL + 3nxL = -1lnx

Add 'lnx' to each side of the equation.
-5ln + -7nL + lnx + 3nxL = -1lnx + lnx

Reorder the terms:
-5ln + lnx + -7nL + 3nxL = -1lnx + lnx

Combine like terms: -1lnx + lnx = 0
-5ln + lnx + -7nL + 3nxL = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(-5l + lx + -7L + 3xL) = 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 + lx + -7L + 3xL)' equal to zero and attempt to solve:

Simplifying
-5l + lx + -7L + 3xL = 0

Reorder the terms:
-7L + -5l + lx + 3xL = 0

Solving
-7L + -5l + lx + 3xL = 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 + lx + 7L + 3xL = 0 + 7L

Reorder the terms:
-7L + 7L + -5l + lx + 3xL = 0 + 7L

Combine like terms: -7L + 7L = 0
0 + -5l + lx + 3xL = 0 + 7L
-5l + lx + 3xL = 0 + 7L
Remove the zero:
-5l + lx + 3xL = 7L

Add '5l' to each side of the equation.
-5l + lx + 5l + 3xL = 7L + 5l

Reorder the terms:
-5l + 5l + lx + 3xL = 7L + 5l

Combine like terms: -5l + 5l = 0
0 + lx + 3xL = 7L + 5l
lx + 3xL = 7L + 5l

Add '-1lx' to each side of the equation.
lx + -1lx + 3xL = 7L + 5l + -1lx

Combine like terms: lx + -1lx = 0
0 + 3xL = 7L + 5l + -1lx
3xL = 7L + 5l + -1lx

Add '-3xL' to each side of the equation.
3xL + -3xL = 7L + 5l + -1lx + -3xL

Combine like terms: 3xL + -3xL = 0
0 = 7L + 5l + -1lx + -3xL

Simplifying
0 = 7L + 5l + -1lx + -3xL

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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