ln(x+2)+ln(x-2)=ln(9x-24)

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Solution for ln(x+2)+ln(x-2)=ln(9x-24) equation:


Simplifying
ln(x + 2) + ln(x + -2) = ln(9x + -24)

Reorder the terms:
ln(2 + x) + ln(x + -2) = ln(9x + -24)
(2 * ln + x * ln) + ln(x + -2) = ln(9x + -24)
(2ln + lnx) + ln(x + -2) = ln(9x + -24)

Reorder the terms:
2ln + lnx + ln(-2 + x) = ln(9x + -24)
2ln + lnx + (-2 * ln + x * ln) = ln(9x + -24)
2ln + lnx + (-2ln + lnx) = ln(9x + -24)

Reorder the terms:
2ln + -2ln + lnx + lnx = ln(9x + -24)

Combine like terms: 2ln + -2ln = 0
0 + lnx + lnx = ln(9x + -24)
lnx + lnx = ln(9x + -24)

Combine like terms: lnx + lnx = 2lnx
2lnx = ln(9x + -24)

Reorder the terms:
2lnx = ln(-24 + 9x)
2lnx = (-24 * ln + 9x * ln)
2lnx = (-24ln + 9lnx)

Solving
2lnx = -24ln + 9lnx

Solving for variable 'l'.

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

Add '24ln' to each side of the equation.
24ln + 2lnx = -24ln + 24ln + 9lnx

Combine like terms: -24ln + 24ln = 0
24ln + 2lnx = 0 + 9lnx
24ln + 2lnx = 9lnx

Add '-9lnx' to each side of the equation.
24ln + 2lnx + -9lnx = 9lnx + -9lnx

Combine like terms: 2lnx + -9lnx = -7lnx
24ln + -7lnx = 9lnx + -9lnx

Combine like terms: 9lnx + -9lnx = 0
24ln + -7lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(24 + -7x) = 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 '(24 + -7x)' equal to zero and attempt to solve: Simplifying 24 + -7x = 0 Solving 24 + -7x = 0 Move all terms containing l to the left, all other terms to the right. Add '-24' to each side of the equation. 24 + -24 + -7x = 0 + -24 Combine like terms: 24 + -24 = 0 0 + -7x = 0 + -24 -7x = 0 + -24 Combine like terms: 0 + -24 = -24 -7x = -24 Add '7x' to each side of the equation. -7x + 7x = -24 + 7x Combine like terms: -7x + 7x = 0 0 = -24 + 7x Simplifying 0 = -24 + 7x 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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