ln(x-1)-ln(6-x)=0

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Solution for ln(x-1)-ln(6-x)=0 equation: 


Simplifying
ln(x + -1) + -1ln(6 + -1x) = 0

Reorder the terms:
ln(-1 + x) + -1ln(6 + -1x) = 0
(-1 * ln + x * ln) + -1ln(6 + -1x) = 0
(-1ln + lnx) + -1ln(6 + -1x) = 0
-1ln + lnx + (6 * -1ln + -1x * -1ln) = 0
-1ln + lnx + (-6ln + 1lnx) = 0

Reorder the terms:
-1ln + -6ln + lnx + 1lnx = 0

Combine like terms: -1ln + -6ln = -7ln
-7ln + lnx + 1lnx = 0

Combine like terms: lnx + 1lnx = 2lnx
-7ln + 2lnx = 0

Solving
-7ln + 2lnx = 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(-7 + 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 '(-7 + 2x)' equal to zero and attempt to solve:

Simplifying
-7 + 2x = 0

Solving
-7 + 2x = 0

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

Add '7' to each side of the equation.
-7 + 7 + 2x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + 2x = 0 + 7
2x = 0 + 7

Combine like terms: 0 + 7 = 7
2x = 7

Add '-2x' to each side of the equation.
2x + -2x = 7 + -2x

Combine like terms: 2x + -2x = 0
0 = 7 + -2x

Simplifying
0 = 7 + -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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