3ln(x-2)=ln(x+1)

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Solution for 3ln(x-2)=ln(x+1) equation:


Simplifying
3ln(x + -2) = ln(x + 1)

Reorder the terms:
3ln(-2 + x) = ln(x + 1)
(-2 * 3ln + x * 3ln) = ln(x + 1)
(-6ln + 3lnx) = ln(x + 1)

Reorder the terms:
-6ln + 3lnx = ln(1 + x)
-6ln + 3lnx = (1 * ln + x * ln)
-6ln + 3lnx = (1ln + lnx)

Solving
-6ln + 3lnx = 1ln + lnx

Solving for variable 'l'.

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

Add '-1ln' to each side of the equation.
-6ln + -1ln + 3lnx = 1ln + -1ln + lnx

Combine like terms: -6ln + -1ln = -7ln
-7ln + 3lnx = 1ln + -1ln + lnx

Combine like terms: 1ln + -1ln = 0
-7ln + 3lnx = 0 + lnx
-7ln + 3lnx = lnx

Add '-1lnx' to each side of the equation.
-7ln + 3lnx + -1lnx = lnx + -1lnx

Combine like terms: 3lnx + -1lnx = 2lnx
-7ln + 2lnx = lnx + -1lnx

Combine like terms: lnx + -1lnx = 0
-7ln + 2lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-7 + 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 '(-7 + 2x)' equal to zero and attempt to solve: Simplifying -7 + 2x = 0 Solving -7 + 2x = 0 Move all terms containing l to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + 2x = 0 + 7 Combine like terms: -7 + 7 = 0 0 + 2x = 0 + 7 2x = 0 + 7 Combine like terms: 0 + 7 = 7 2x = 7 Add '-2x' to each side of the equation. 2x + -2x = 7 + -2x Combine like terms: 2x + -2x = 0 0 = 7 + -2x Simplifying 0 = 7 + -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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