ln(x^2-8x+14)=ln(x-4)+ln(x-2)

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Solution for ln(x^2-8x+14)=ln(x-4)+ln(x-2) equation: 


Simplifying
ln(x2 + -8x + 14) = ln(x + -4) + ln(x + -2)

Reorder the terms:
ln(14 + -8x + x2) = ln(x + -4) + ln(x + -2)
(14 * ln + -8x * ln + x2 * ln) = ln(x + -4) + ln(x + -2)
(14ln + -8lnx + lnx2) = ln(x + -4) + ln(x + -2)

Reorder the terms:
14ln + -8lnx + lnx2 = ln(-4 + x) + ln(x + -2)
14ln + -8lnx + lnx2 = (-4 * ln + x * ln) + ln(x + -2)
14ln + -8lnx + lnx2 = (-4ln + lnx) + ln(x + -2)

Reorder the terms:
14ln + -8lnx + lnx2 = -4ln + lnx + ln(-2 + x)
14ln + -8lnx + lnx2 = -4ln + lnx + (-2 * ln + x * ln)
14ln + -8lnx + lnx2 = -4ln + lnx + (-2ln + lnx)

Reorder the terms:
14ln + -8lnx + lnx2 = -4ln + -2ln + lnx + lnx

Combine like terms: -4ln + -2ln = -6ln
14ln + -8lnx + lnx2 = -6ln + lnx + lnx

Combine like terms: lnx + lnx = 2lnx
14ln + -8lnx + lnx2 = -6ln + 2lnx

Solving
14ln + -8lnx + lnx2 = -6ln + 2lnx

Solving for variable 'l'.

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

Add '6ln' to each side of the equation.
14ln + -8lnx + 6ln + lnx2 = -6ln + 6ln + 2lnx

Reorder the terms:
14ln + 6ln + -8lnx + lnx2 = -6ln + 6ln + 2lnx

Combine like terms: 14ln + 6ln = 20ln
20ln + -8lnx + lnx2 = -6ln + 6ln + 2lnx

Combine like terms: -6ln + 6ln = 0
20ln + -8lnx + lnx2 = 0 + 2lnx
20ln + -8lnx + lnx2 = 2lnx

Add '-2lnx' to each side of the equation.
20ln + -8lnx + -2lnx + lnx2 = 2lnx + -2lnx

Combine like terms: -8lnx + -2lnx = -10lnx
20ln + -10lnx + lnx2 = 2lnx + -2lnx

Combine like terms: 2lnx + -2lnx = 0
20ln + -10lnx + lnx2 = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(20 + -10x + 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 '(20 + -10x + x2)' equal to zero and attempt to solve:

Simplifying
20 + -10x + x2 = 0

Solving
20 + -10x + x2 = 0

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

Add '-20' to each side of the equation.
20 + -10x + -20 + x2 = 0 + -20

Reorder the terms:
20 + -20 + -10x + x2 = 0 + -20

Combine like terms: 20 + -20 = 0
0 + -10x + x2 = 0 + -20
-10x + x2 = 0 + -20

Combine like terms: 0 + -20 = -20
-10x + x2 = -20

Add '10x' to each side of the equation.
-10x + 10x + x2 = -20 + 10x

Combine like terms: -10x + 10x = 0
0 + x2 = -20 + 10x
x2 = -20 + 10x

Add '-1x2' to each side of the equation.
x2 + -1x2 = -20 + 10x + -1x2

Combine like terms: x2 + -1x2 = 0
0 = -20 + 10x + -1x2

Simplifying
0 = -20 + 10x + -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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