2ln(x-1)=ln(-4x+16)

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Solution for 2ln(x-1)=ln(-4x+16) equation:


Simplifying
2ln(x + -1) = ln(-4x + 16)

Reorder the terms:
2ln(-1 + x) = ln(-4x + 16)
(-1 * 2ln + x * 2ln) = ln(-4x + 16)
(-2ln + 2lnx) = ln(-4x + 16)

Reorder the terms:
-2ln + 2lnx = ln(16 + -4x)
-2ln + 2lnx = (16 * ln + -4x * ln)
-2ln + 2lnx = (16ln + -4lnx)

Solving
-2ln + 2lnx = 16ln + -4lnx

Solving for variable 'l'.

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

Add '-16ln' to each side of the equation.
-2ln + -16ln + 2lnx = 16ln + -16ln + -4lnx

Combine like terms: -2ln + -16ln = -18ln
-18ln + 2lnx = 16ln + -16ln + -4lnx

Combine like terms: 16ln + -16ln = 0
-18ln + 2lnx = 0 + -4lnx
-18ln + 2lnx = -4lnx

Add '4lnx' to each side of the equation.
-18ln + 2lnx + 4lnx = -4lnx + 4lnx

Combine like terms: 2lnx + 4lnx = 6lnx
-18ln + 6lnx = -4lnx + 4lnx

Combine like terms: -4lnx + 4lnx = 0
-18ln + 6lnx = 0

Factor out the Greatest Common Factor (GCF), '6ln'.
6ln(-3 + x) = 0

Ignore the factor 6.

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 '(-3 + x)' equal to zero and attempt to solve: Simplifying -3 + x = 0 Solving -3 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + x = 0 + 3 x = 0 + 3 Combine like terms: 0 + 3 = 3 x = 3 Add '-1x' to each side of the equation. x + -1x = 3 + -1x Combine like terms: x + -1x = 0 0 = 3 + -1x Simplifying 0 = 3 + -1x 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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