(x-8)ln(x-8)=0

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Solution for (x-8)ln(x-8)=0 equation:


Simplifying
(x + -8) * ln(x + -8) = 0

Reorder the terms:
(-8 + x) * ln(x + -8) = 0

Reorder the terms:
(-8 + x) * ln(-8 + x) = 0

Reorder the terms for easier multiplication:
ln(-8 + x)(-8 + x) = 0

Multiply (-8 + x) * (-8 + x)
ln(-8(-8 + x) + x(-8 + x)) = 0
ln((-8 * -8 + x * -8) + x(-8 + x)) = 0
ln((64 + -8x) + x(-8 + x)) = 0
ln(64 + -8x + (-8 * x + x * x)) = 0
ln(64 + -8x + (-8x + x2)) = 0

Combine like terms: -8x + -8x = -16x
ln(64 + -16x + x2) = 0
(64 * ln + -16x * ln + x2 * ln) = 0
(64ln + -16lnx + lnx2) = 0

Solving
64ln + -16lnx + lnx2 = 0

Solving for variable 'l'.

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

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(64 + -16x + x2) = 0

Factor a trinomial.
ln((8 + -1x)(8 + -1x)) = 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 '(8 + -1x)' equal to zero and attempt to solve: Simplifying 8 + -1x = 0 Solving 8 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1x = 0 + -8 -1x = 0 + -8 Combine like terms: 0 + -8 = -8 -1x = -8 Add 'x' to each side of the equation. -1x + x = -8 + x Combine like terms: -1x + x = 0 0 = -8 + x Simplifying 0 = -8 + x The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.

Subproblem 3

Set the factor '(8 + -1x)' equal to zero and attempt to solve: Simplifying 8 + -1x = 0 Solving 8 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1x = 0 + -8 -1x = 0 + -8 Combine like terms: 0 + -8 = -8 -1x = -8 Add 'x' to each side of the equation. -1x + x = -8 + x Combine like terms: -1x + x = 0 0 = -8 + x Simplifying 0 = -8 + x 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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