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

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


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

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

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

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

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

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

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.
-2ln + 4ln + 2lnx = -4ln + 4ln + lnx

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

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

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

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

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

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