ln(3x+4)=2ln(x+1)

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Solution for ln(3x+4)=2ln(x+1) equation:


Simplifying
ln(3x + 4) = 2ln(x + 1)

Reorder the terms:
ln(4 + 3x) = 2ln(x + 1)
(4 * ln + 3x * ln) = 2ln(x + 1)
(4ln + 3lnx) = 2ln(x + 1)

Reorder the terms:
4ln + 3lnx = 2ln(1 + x)
4ln + 3lnx = (1 * 2ln + x * 2ln)
4ln + 3lnx = (2ln + 2lnx)

Solving
4ln + 3lnx = 2ln + 2lnx

Solving for variable 'l'.

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

Add '-2ln' to each side of the equation.
4ln + -2ln + 3lnx = 2ln + -2ln + 2lnx

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

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

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

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

Combine like terms: 2lnx + -2lnx = 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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