2ln(x-4)=ln(x+6)+ln(5)

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Solution for 2ln(x-4)=ln(x+6)+ln(5) equation:


Simplifying
2ln(x + -4) = ln(x + 6) + ln(5)

Reorder the terms:
2ln(-4 + x) = ln(x + 6) + ln(5)
(-4 * 2ln + x * 2ln) = ln(x + 6) + ln(5)
(-8ln + 2lnx) = ln(x + 6) + ln(5)

Reorder the terms:
-8ln + 2lnx = ln(6 + x) + ln(5)
-8ln + 2lnx = (6 * ln + x * ln) + ln(5)
-8ln + 2lnx = (6ln + lnx) + ln(5)

Reorder the terms for easier multiplication:
-8ln + 2lnx = 6ln + lnx + 5ln

Reorder the terms:
-8ln + 2lnx = 6ln + 5ln + lnx

Combine like terms: 6ln + 5ln = 11ln
-8ln + 2lnx = 11ln + lnx

Solving
-8ln + 2lnx = 11ln + lnx

Solving for variable 'l'.

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

Add '-11ln' to each side of the equation.
-8ln + -11ln + 2lnx = 11ln + -11ln + lnx

Combine like terms: -8ln + -11ln = -19ln
-19ln + 2lnx = 11ln + -11ln + lnx

Combine like terms: 11ln + -11ln = 0
-19ln + 2lnx = 0 + lnx
-19ln + 2lnx = lnx

Add '-1lnx' to each side of the equation.
-19ln + 2lnx + -1lnx = lnx + -1lnx

Combine like terms: 2lnx + -1lnx = 1lnx
-19ln + 1lnx = lnx + -1lnx

Combine like terms: lnx + -1lnx = 0
-19ln + 1lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-19 + 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 '(-19 + x)' equal to zero and attempt to solve: Simplifying -19 + x = 0 Solving -19 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '19' to each side of the equation. -19 + 19 + x = 0 + 19 Combine like terms: -19 + 19 = 0 0 + x = 0 + 19 x = 0 + 19 Combine like terms: 0 + 19 = 19 x = 19 Add '-1x' to each side of the equation. x + -1x = 19 + -1x Combine like terms: x + -1x = 0 0 = 19 + -1x Simplifying 0 = 19 + -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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