ln(x+3)+ln(x-2)=ln(24)

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Solution for ln(x+3)+ln(x-2)=ln(24) equation:


Simplifying
ln(x + 3) + ln(x + -2) = ln(24)

Reorder the terms:
ln(3 + x) + ln(x + -2) = ln(24)
(3 * ln + x * ln) + ln(x + -2) = ln(24)
(3ln + lnx) + ln(x + -2) = ln(24)

Reorder the terms:
3ln + lnx + ln(-2 + x) = ln(24)
3ln + lnx + (-2 * ln + x * ln) = ln(24)
3ln + lnx + (-2ln + lnx) = ln(24)

Reorder the terms:
3ln + -2ln + lnx + lnx = ln(24)

Combine like terms: 3ln + -2ln = 1ln
1ln + lnx + lnx = ln(24)

Combine like terms: lnx + lnx = 2lnx
1ln + 2lnx = ln(24)

Reorder the terms for easier multiplication:
1ln + 2lnx = 24ln

Solving
1ln + 2lnx = 24ln

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.
1ln + -24ln + 2lnx = 24ln + -24ln

Combine like terms: 1ln + -24ln = -23ln
-23ln + 2lnx = 24ln + -24ln

Combine like terms: 24ln + -24ln = 0
-23ln + 2lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-23 + 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 '(-23 + 2x)' equal to zero and attempt to solve: Simplifying -23 + 2x = 0 Solving -23 + 2x = 0 Move all terms containing l to the left, all other terms to the right. Add '23' to each side of the equation. -23 + 23 + 2x = 0 + 23 Combine like terms: -23 + 23 = 0 0 + 2x = 0 + 23 2x = 0 + 23 Combine like terms: 0 + 23 = 23 2x = 23 Add '-2x' to each side of the equation. 2x + -2x = 23 + -2x Combine like terms: 2x + -2x = 0 0 = 23 + -2x Simplifying 0 = 23 + -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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