ln(x)-ln(8-x)=6

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Solution for ln(x)-ln(8-x)=6 equation:


Simplifying
ln(x) + -1ln(8 + -1x) = 6

Multiply ln * x
lnx + -1ln(8 + -1x) = 6
lnx + (8 * -1ln + -1x * -1ln) = 6
lnx + (-8ln + 1lnx) = 6

Reorder the terms:
-8ln + lnx + 1lnx = 6

Combine like terms: lnx + 1lnx = 2lnx
-8ln + 2lnx = 6

Solving
-8ln + 2lnx = 6

Solving for variable 'l'.

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

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

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

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + -4ln + lnx) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-3 + -4ln + lnx)' equal to zero and attempt to solve: Simplifying -3 + -4ln + lnx = 0 Solving -3 + -4ln + lnx = 0 Move all terms containing l to the left, all other terms to the right. Add '3' to each side of the equation. -3 + -4ln + 3 + lnx = 0 + 3 Reorder the terms: -3 + 3 + -4ln + lnx = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -4ln + lnx = 0 + 3 -4ln + lnx = 0 + 3 Combine like terms: 0 + 3 = 3 -4ln + lnx = 3 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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