ln(x+3)+ln(x+1)=ln(x+13)

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Solution for ln(x+3)+ln(x+1)=ln(x+13) equation:


Simplifying
ln(x + 3) + ln(x + 1) = ln(x + 13)

Reorder the terms:
ln(3 + x) + ln(x + 1) = ln(x + 13)
(3 * ln + x * ln) + ln(x + 1) = ln(x + 13)
(3ln + lnx) + ln(x + 1) = ln(x + 13)

Reorder the terms:
3ln + lnx + ln(1 + x) = ln(x + 13)
3ln + lnx + (1 * ln + x * ln) = ln(x + 13)
3ln + lnx + (1ln + lnx) = ln(x + 13)

Reorder the terms:
3ln + 1ln + lnx + lnx = ln(x + 13)

Combine like terms: 3ln + 1ln = 4ln
4ln + lnx + lnx = ln(x + 13)

Combine like terms: lnx + lnx = 2lnx
4ln + 2lnx = ln(x + 13)

Reorder the terms:
4ln + 2lnx = ln(13 + x)
4ln + 2lnx = (13 * ln + x * ln)
4ln + 2lnx = (13ln + lnx)

Solving
4ln + 2lnx = 13ln + lnx

Solving for variable 'l'.

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

Add '-13ln' to each side of the equation.
4ln + -13ln + 2lnx = 13ln + -13ln + lnx

Combine like terms: 4ln + -13ln = -9ln
-9ln + 2lnx = 13ln + -13ln + lnx

Combine like terms: 13ln + -13ln = 0
-9ln + 2lnx = 0 + lnx
-9ln + 2lnx = lnx

Add '-1lnx' to each side of the equation.
-9ln + 2lnx + -1lnx = lnx + -1lnx

Combine like terms: 2lnx + -1lnx = 1lnx
-9ln + 1lnx = lnx + -1lnx

Combine like terms: lnx + -1lnx = 0
-9ln + 1lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-9 + 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 '(-9 + x)' equal to zero and attempt to solve: Simplifying -9 + x = 0 Solving -9 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = 0 + 9 Combine like terms: -9 + 9 = 0 0 + x = 0 + 9 x = 0 + 9 Combine like terms: 0 + 9 = 9 x = 9 Add '-1x' to each side of the equation. x + -1x = 9 + -1x Combine like terms: x + -1x = 0 0 = 9 + -1x Simplifying 0 = 9 + -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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