ln(x-4)=-lnx

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Solution for ln(x-4)=-lnx equation:


Simplifying
ln(x + -4) = -1lnx

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

Solving
-4ln + lnx = -1lnx

Solving for variable 'l'.

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

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

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

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

Factor out the Greatest Common Factor (GCF), '2ln'.
2ln(-2 + x) = 0

Ignore the factor 2.

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