ln(x-13)-2ln(x+1)=-2ln(7)

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Solution for ln(x-13)-2ln(x+1)=-2ln(7) equation:


Simplifying
ln(x + -13) + -2ln(x + 1) = -2ln(7)

Reorder the terms:
ln(-13 + x) + -2ln(x + 1) = -2ln(7)
(-13 * ln + x * ln) + -2ln(x + 1) = -2ln(7)
(-13ln + lnx) + -2ln(x + 1) = -2ln(7)

Reorder the terms:
-13ln + lnx + -2ln(1 + x) = -2ln(7)
-13ln + lnx + (1 * -2ln + x * -2ln) = -2ln(7)
-13ln + lnx + (-2ln + -2lnx) = -2ln(7)

Reorder the terms:
-13ln + -2ln + lnx + -2lnx = -2ln(7)

Combine like terms: -13ln + -2ln = -15ln
-15ln + lnx + -2lnx = -2ln(7)

Combine like terms: lnx + -2lnx = -1lnx
-15ln + -1lnx = -2ln(7)

Reorder the terms for easier multiplication:
-15ln + -1lnx = -2 * 7ln

Multiply -2 * 7
-15ln + -1lnx = -14ln

Solving
-15ln + -1lnx = -14ln

Solving for variable 'l'.

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

Add '14ln' to each side of the equation.
-15ln + 14ln + -1lnx = -14ln + 14ln

Combine like terms: -15ln + 14ln = -1ln
-1ln + -1lnx = -14ln + 14ln

Combine like terms: -14ln + 14ln = 0
-1ln + -1lnx = 0

Factor out the Greatest Common Factor (GCF), '-1ln'.
-1ln(1 + x) = 0

Ignore the factor -1.

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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