ln(x+8)(x-3)=2lnx

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Solution for ln(x+8)(x-3)=2lnx equation:


Simplifying
ln(x + 8)(x + -3) = 2lnx

Reorder the terms:
ln(8 + x)(x + -3) = 2lnx

Reorder the terms:
ln(8 + x)(-3 + x) = 2lnx

Multiply (8 + x) * (-3 + x)
ln(8(-3 + x) + x(-3 + x)) = 2lnx
ln((-3 * 8 + x * 8) + x(-3 + x)) = 2lnx
ln((-24 + 8x) + x(-3 + x)) = 2lnx
ln(-24 + 8x + (-3 * x + x * x)) = 2lnx
ln(-24 + 8x + (-3x + x2)) = 2lnx

Combine like terms: 8x + -3x = 5x
ln(-24 + 5x + x2) = 2lnx
(-24 * ln + 5x * ln + x2 * ln) = 2lnx
(-24ln + 5lnx + lnx2) = 2lnx

Solving
-24ln + 5lnx + lnx2 = 2lnx

Solving for variable 'l'.

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

Add '-2lnx' to each side of the equation.
-24ln + 5lnx + -2lnx + lnx2 = 2lnx + -2lnx

Combine like terms: 5lnx + -2lnx = 3lnx
-24ln + 3lnx + lnx2 = 2lnx + -2lnx

Combine like terms: 2lnx + -2lnx = 0
-24ln + 3lnx + lnx2 = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-24 + 3x + x2) = 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 + 3x + x2)' equal to zero and attempt to solve: Simplifying -24 + 3x + x2 = 0 Solving -24 + 3x + x2 = 0 Move all terms containing l to the left, all other terms to the right. Add '24' to each side of the equation. -24 + 3x + 24 + x2 = 0 + 24 Reorder the terms: -24 + 24 + 3x + x2 = 0 + 24 Combine like terms: -24 + 24 = 0 0 + 3x + x2 = 0 + 24 3x + x2 = 0 + 24 Combine like terms: 0 + 24 = 24 3x + x2 = 24 Add '-3x' to each side of the equation. 3x + -3x + x2 = 24 + -3x Combine like terms: 3x + -3x = 0 0 + x2 = 24 + -3x x2 = 24 + -3x Add '-1x2' to each side of the equation. x2 + -1x2 = 24 + -3x + -1x2 Combine like terms: x2 + -1x2 = 0 0 = 24 + -3x + -1x2 Simplifying 0 = 24 + -3x + -1x2 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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