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

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


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

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

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

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

Combine like terms: 3ln + 2ln = 5ln
5ln + lnx + lnx = ln(x + 4)

Combine like terms: lnx + lnx = 2lnx
5ln + 2lnx = ln(x + 4)

Reorder the terms:
5ln + 2lnx = ln(4 + x)
5ln + 2lnx = (4 * ln + x * ln)
5ln + 2lnx = (4ln + lnx)

Solving
5ln + 2lnx = 4ln + lnx

Solving for variable 'l'.

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

Add '-4ln' to each side of the equation.
5ln + -4ln + 2lnx = 4ln + -4ln + lnx

Combine like terms: 5ln + -4ln = 1ln
1ln + 2lnx = 4ln + -4ln + lnx

Combine like terms: 4ln + -4ln = 0
1ln + 2lnx = 0 + lnx
1ln + 2lnx = lnx

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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