Ln(3x-7)=ln(2x)

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Solution for Ln(3x-7)=ln(2x) equation: 


Simplifying
Ln(3x + -7) = ln(2x)

Reorder the terms:
nL(-7 + 3x) = ln(2x)
(-7 * nL + 3x * nL) = ln(2x)
(-7nL + 3nxL) = ln(2x)

Remove parenthesis around (2x)
-7nL + 3nxL = ln * 2x

Reorder the terms for easier multiplication:
-7nL + 3nxL = 2ln * x

Multiply ln * x
-7nL + 3nxL = 2lnx

Solving
-7nL + 3nxL = 2lnx

Solving for variable 'n'.

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

Add '-2lnx' to each side of the equation.
-7nL + -2lnx + 3nxL = 2lnx + -2lnx

Reorder the terms:
-2lnx + -7nL + 3nxL = 2lnx + -2lnx

Combine like terms: 2lnx + -2lnx = 0
-2lnx + -7nL + 3nxL = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(-2lx + -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 '(-2lx + -7L + 3xL)' equal to zero and attempt to solve:

Simplifying
-2lx + -7L + 3xL = 0

Reorder the terms:
-7L + -2lx + 3xL = 0

Solving
-7L + -2lx + 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 + -2lx + 7L + 3xL = 0 + 7L

Reorder the terms:
-7L + 7L + -2lx + 3xL = 0 + 7L

Combine like terms: -7L + 7L = 0
0 + -2lx + 3xL = 0 + 7L
-2lx + 3xL = 0 + 7L
Remove the zero:
-2lx + 3xL = 7L

Add '2lx' to each side of the equation.
-2lx + 2lx + 3xL = 7L + 2lx

Combine like terms: -2lx + 2lx = 0
0 + 3xL = 7L + 2lx
3xL = 7L + 2lx

Add '-3xL' to each side of the equation.
3xL + -3xL = 7L + 2lx + -3xL

Combine like terms: 3xL + -3xL = 0
0 = 7L + 2lx + -3xL

Simplifying
0 = 7L + 2lx + -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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