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

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


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

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

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

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

Solving for variable 'l'.

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

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

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

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

Add '-4lnx' to each side of the equation.
7ln + 2lnx + -4lnx = 4lnx + -4lnx

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

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

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(7 + -2x) = 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 + -2x)' equal to zero and attempt to solve: Simplifying 7 + -2x = 0 Solving 7 + -2x = 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 + -2x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -2x = 0 + -7 -2x = 0 + -7 Combine like terms: 0 + -7 = -7 -2x = -7 Add '2x' to each side of the equation. -2x + 2x = -7 + 2x Combine like terms: -2x + 2x = 0 0 = -7 + 2x Simplifying 0 = -7 + 2x 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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