ln(x+1)+ln(x-2)=lnx

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


Simplifying
ln(x + 1) + ln(x + -2) = lnx

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

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

Reorder the terms:
1ln + -2ln + lnx + lnx = lnx

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

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

Solving
-1ln + 2lnx = lnx

Solving for variable 'l'.

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

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

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

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

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