ln(x+2)+ln(x-2)=ln(9)

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Solution for ln(x+2)+ln(x-2)=ln(9) equation:


Simplifying
ln(x + 2) + ln(x + -2) = ln(9)

Reorder the terms:
ln(2 + x) + ln(x + -2) = ln(9)
(2 * ln + x * ln) + ln(x + -2) = ln(9)
(2ln + lnx) + ln(x + -2) = ln(9)

Reorder the terms:
2ln + lnx + ln(-2 + x) = ln(9)
2ln + lnx + (-2 * ln + x * ln) = ln(9)
2ln + lnx + (-2ln + lnx) = ln(9)

Reorder the terms:
2ln + -2ln + lnx + lnx = ln(9)

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

Combine like terms: lnx + lnx = 2lnx
2lnx = ln(9)

Reorder the terms for easier multiplication:
2lnx = 9ln

Solving
2lnx = 9ln

Solving for variable 'l'.

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

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

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

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-9 + 2x) = 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 + 2x)' equal to zero and attempt to solve: Simplifying -9 + 2x = 0 Solving -9 + 2x = 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 + 2x = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 2x = 0 + 9 2x = 0 + 9 Combine like terms: 0 + 9 = 9 2x = 9 Add '-2x' to each side of the equation. 2x + -2x = 9 + -2x Combine like terms: 2x + -2x = 0 0 = 9 + -2x Simplifying 0 = 9 + -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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