Ln(5x-7)=ln(3x+13)

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Solution for Ln(5x-7)=ln(3x+13) equation: 


Simplifying
Ln(5x + -7) = ln(3x + 13)

Reorder the terms:
nL(-7 + 5x) = ln(3x + 13)
(-7 * nL + 5x * nL) = ln(3x + 13)
(-7nL + 5nxL) = ln(3x + 13)

Reorder the terms:
-7nL + 5nxL = ln(13 + 3x)
-7nL + 5nxL = (13 * ln + 3x * ln)
-7nL + 5nxL = (13ln + 3lnx)

Solving
-7nL + 5nxL = 13ln + 3lnx

Solving for variable 'n'.

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

Add '-13ln' to each side of the equation.
-7nL + -13ln + 5nxL = 13ln + -13ln + 3lnx

Reorder the terms:
-13ln + -7nL + 5nxL = 13ln + -13ln + 3lnx

Combine like terms: 13ln + -13ln = 0
-13ln + -7nL + 5nxL = 0 + 3lnx
-13ln + -7nL + 5nxL = 3lnx

Add '-3lnx' to each side of the equation.
-13ln + -7nL + -3lnx + 5nxL = 3lnx + -3lnx

Reorder the terms:
-13ln + -3lnx + -7nL + 5nxL = 3lnx + -3lnx

Combine like terms: 3lnx + -3lnx = 0
-13ln + -3lnx + -7nL + 5nxL = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(-13l + -3lx + -7L + 5xL) = 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 '(-13l + -3lx + -7L + 5xL)' equal to zero and attempt to solve:

Simplifying
-13l + -3lx + -7L + 5xL = 0

Reorder the terms:
-7L + -13l + -3lx + 5xL = 0

Solving
-7L + -13l + -3lx + 5xL = 0

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

Add '7L' to each side of the equation.
-7L + -13l + -3lx + 7L + 5xL = 0 + 7L

Reorder the terms:
-7L + 7L + -13l + -3lx + 5xL = 0 + 7L

Combine like terms: -7L + 7L = 0
0 + -13l + -3lx + 5xL = 0 + 7L
-13l + -3lx + 5xL = 0 + 7L
Remove the zero:
-13l + -3lx + 5xL = 7L

Add '13l' to each side of the equation.
-13l + -3lx + 13l + 5xL = 7L + 13l

Reorder the terms:
-13l + 13l + -3lx + 5xL = 7L + 13l

Combine like terms: -13l + 13l = 0
0 + -3lx + 5xL = 7L + 13l
-3lx + 5xL = 7L + 13l

Add '3lx' to each side of the equation.
-3lx + 3lx + 5xL = 7L + 13l + 3lx

Combine like terms: -3lx + 3lx = 0
0 + 5xL = 7L + 13l + 3lx
5xL = 7L + 13l + 3lx

Add '-5xL' to each side of the equation.
5xL + -5xL = 7L + 13l + 3lx + -5xL

Combine like terms: 5xL + -5xL = 0
0 = 7L + 13l + 3lx + -5xL

Simplifying
0 = 7L + 13l + 3lx + -5xL

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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