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

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


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

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

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

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

Solving for variable 'l'.

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

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

Combine like terms: -1ln + -3ln = -4ln
-4ln + 3lnx = 3ln + -3ln + lnx

Combine like terms: 3ln + -3ln = 0
-4ln + 3lnx = 0 + lnx
-4ln + 3lnx = lnx

Add '-1lnx' to each side of the equation.
-4ln + 3lnx + -1lnx = lnx + -1lnx

Combine like terms: 3lnx + -1lnx = 2lnx
-4ln + 2lnx = lnx + -1lnx

Combine like terms: lnx + -1lnx = 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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