ln(x+4)+ln(x-2)=ln^16

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Solution for ln(x+4)+ln(x-2)=ln^16 equation:


Simplifying
ln(x + 4) + ln(x + -2) = ln16

Reorder the terms:
ln(4 + x) + ln(x + -2) = ln16
(4 * ln + x * ln) + ln(x + -2) = ln16
(4ln + lnx) + ln(x + -2) = ln16

Reorder the terms:
4ln + lnx + ln(-2 + x) = ln16
4ln + lnx + (-2 * ln + x * ln) = ln16
4ln + lnx + (-2ln + lnx) = ln16

Reorder the terms:
4ln + -2ln + lnx + lnx = ln16

Combine like terms: 4ln + -2ln = 2ln
2ln + lnx + lnx = ln16

Combine like terms: lnx + lnx = 2lnx
2ln + 2lnx = ln16

Solving
2ln + 2lnx = ln16

Solving for variable 'l'.

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

Add '-1ln16' to each side of the equation.
2ln + 2lnx + -1ln16 = ln16 + -1ln16

Combine like terms: ln16 + -1ln16 = 0
2ln + 2lnx + -1ln16 = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(2 + 2x + -1n15) = 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 '(2 + 2x + -1n15)' equal to zero and attempt to solve: Simplifying 2 + 2x + -1n15 = 0 Reorder the terms: 2 + -1n15 + 2x = 0 Solving 2 + -1n15 + 2x = 0 Move all terms containing l to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -1n15 + -2 + 2x = 0 + -2 Reorder the terms: 2 + -2 + -1n15 + 2x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1n15 + 2x = 0 + -2 -1n15 + 2x = 0 + -2 Combine like terms: 0 + -2 = -2 -1n15 + 2x = -2 Add 'n15' to each side of the equation. -1n15 + n15 + 2x = -2 + n15 Combine like terms: -1n15 + n15 = 0 0 + 2x = -2 + n15 2x = -2 + n15 Add '-2x' to each side of the equation. 2x + -2x = -2 + n15 + -2x Combine like terms: 2x + -2x = 0 0 = -2 + n15 + -2x Simplifying 0 = -2 + n15 + -2x 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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