ln(7-x)+ln(-4-x)=ln(2-4x)

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Solution for ln(7-x)+ln(-4-x)=ln(2-4x) equation:


Simplifying
ln(7 + -1x) + ln(-4 + -1x) = ln(2 + -4x)
(7 * ln + -1x * ln) + ln(-4 + -1x) = ln(2 + -4x)
(7ln + -1lnx) + ln(-4 + -1x) = ln(2 + -4x)
7ln + -1lnx + (-4 * ln + -1x * ln) = ln(2 + -4x)
7ln + -1lnx + (-4ln + -1lnx) = ln(2 + -4x)

Reorder the terms:
7ln + -4ln + -1lnx + -1lnx = ln(2 + -4x)

Combine like terms: 7ln + -4ln = 3ln
3ln + -1lnx + -1lnx = ln(2 + -4x)

Combine like terms: -1lnx + -1lnx = -2lnx
3ln + -2lnx = ln(2 + -4x)
3ln + -2lnx = (2 * ln + -4x * ln)
3ln + -2lnx = (2ln + -4lnx)

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

Solving for variable 'l'.

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

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

Combine like terms: 3ln + -2ln = 1ln
1ln + -2lnx = 2ln + -2ln + -4lnx

Combine like terms: 2ln + -2ln = 0
1ln + -2lnx = 0 + -4lnx
1ln + -2lnx = -4lnx

Add '4lnx' to each side of the equation.
1ln + -2lnx + 4lnx = -4lnx + 4lnx

Combine like terms: -2lnx + 4lnx = 2lnx
1ln + 2lnx = -4lnx + 4lnx

Combine like terms: -4lnx + 4lnx = 0
1ln + 2lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(1 + 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 '(1 + 2x)' equal to zero and attempt to solve: Simplifying 1 + 2x = 0 Solving 1 + 2x = 0 Move all terms containing l to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2x = 0 + -1 2x = 0 + -1 Combine like terms: 0 + -1 = -1 2x = -1 Add '-2x' to each side of the equation. 2x + -2x = -1 + -2x Combine like terms: 2x + -2x = 0 0 = -1 + -2x Simplifying 0 = -1 + -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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