ln(5x+3)=ln(2x-4)

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Solution for ln(5x+3)=ln(2x-4) equation: 


Simplifying
ln(5x + 3) = ln(2x + -4)

Reorder the terms:
ln(3 + 5x) = ln(2x + -4)
(3 * ln + 5x * ln) = ln(2x + -4)
(3ln + 5lnx) = ln(2x + -4)

Reorder the terms:
3ln + 5lnx = ln(-4 + 2x)
3ln + 5lnx = (-4 * ln + 2x * ln)
3ln + 5lnx = (-4ln + 2lnx)

Solving
3ln + 5lnx = -4ln + 2lnx

Solving for variable 'l'.

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

Add '4ln' to each side of the equation.
3ln + 4ln + 5lnx = -4ln + 4ln + 2lnx

Combine like terms: 3ln + 4ln = 7ln
7ln + 5lnx = -4ln + 4ln + 2lnx

Combine like terms: -4ln + 4ln = 0
7ln + 5lnx = 0 + 2lnx
7ln + 5lnx = 2lnx

Add '-2lnx' to each side of the equation.
7ln + 5lnx + -2lnx = 2lnx + -2lnx

Combine like terms: 5lnx + -2lnx = 3lnx
7ln + 3lnx = 2lnx + -2lnx

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

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(7 + 3x) = 0


Subproblem 1
Set the factor 'ln' equal to zero and attempt to solve:

Simplifying
ln = 0

Solving
ln = 0

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

Simplifying
ln = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 2
Set the factor '(7 + 3x)' equal to zero and attempt to solve:

Simplifying
7 + 3x = 0

Solving
7 + 3x = 0

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

Add '-7' to each side of the equation.
7 + -7 + 3x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 3x = 0 + -7
3x = 0 + -7

Combine like terms: 0 + -7 = -7
3x = -7

Add '-3x' to each side of the equation.
3x + -3x = -7 + -3x

Combine like terms: 3x + -3x = 0
0 = -7 + -3x

Simplifying
0 = -7 + -3x

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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