ln(x+6)+ln(x+5)=ln(5)

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Solution for ln(x+6)+ln(x+5)=ln(5) equation:


Simplifying
ln(x + 6) + ln(x + 5) = ln(5)

Reorder the terms:
ln(6 + x) + ln(x + 5) = ln(5)
(6 * ln + x * ln) + ln(x + 5) = ln(5)
(6ln + lnx) + ln(x + 5) = ln(5)

Reorder the terms:
6ln + lnx + ln(5 + x) = ln(5)
6ln + lnx + (5 * ln + x * ln) = ln(5)
6ln + lnx + (5ln + lnx) = ln(5)

Reorder the terms:
6ln + 5ln + lnx + lnx = ln(5)

Combine like terms: 6ln + 5ln = 11ln
11ln + lnx + lnx = ln(5)

Combine like terms: lnx + lnx = 2lnx
11ln + 2lnx = ln(5)

Reorder the terms for easier multiplication:
11ln + 2lnx = 5ln

Solving
11ln + 2lnx = 5ln

Solving for variable 'l'.

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

Add '-5ln' to each side of the equation.
11ln + -5ln + 2lnx = 5ln + -5ln

Combine like terms: 11ln + -5ln = 6ln
6ln + 2lnx = 5ln + -5ln

Combine like terms: 5ln + -5ln = 0
6ln + 2lnx = 0

Factor out the Greatest Common Factor (GCF), '2ln'.
2ln(3 + 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 '(3 + x)' equal to zero and attempt to solve: Simplifying 3 + x = 0 Solving 3 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0 + -3 x = 0 + -3 Combine like terms: 0 + -3 = -3 x = -3 Add '-1x' to each side of the equation. x + -1x = -3 + -1x Combine like terms: x + -1x = 0 0 = -3 + -1x Simplifying 0 = -3 + -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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