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

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


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

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

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

Solving
1ln + lnx = 3ln + 3lnx

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 + lnx = 3ln + -3ln + 3lnx

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

Combine like terms: 3ln + -3ln = 0
-2ln + lnx = 0 + 3lnx
-2ln + lnx = 3lnx

Add '-3lnx' to each side of the equation.
-2ln + lnx + -3lnx = 3lnx + -3lnx

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

Combine like terms: 3lnx + -3lnx = 0
-2ln + -2lnx = 0

Factor out the Greatest Common Factor (GCF), '-2ln'.
-2ln(1 + 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 '(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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