ln(x+5)+ln(x-6)-ln(x)=ln(6)

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Solution for ln(x+5)+ln(x-6)-ln(x)=ln(6) equation: 


Simplifying
ln(x + 5) + ln(x + -6) + -1ln(x) = ln(6)

Reorder the terms:
ln(5 + x) + ln(x + -6) + -1ln(x) = ln(6)
(5 * ln + x * ln) + ln(x + -6) + -1ln(x) = ln(6)
(5ln + lnx) + ln(x + -6) + -1ln(x) = ln(6)

Reorder the terms:
5ln + lnx + ln(-6 + x) + -1ln(x) = ln(6)
5ln + lnx + (-6 * ln + x * ln) + -1ln(x) = ln(6)
5ln + lnx + (-6ln + lnx) + -1ln(x) = ln(6)

Multiply ln * x
5ln + lnx + -6ln + lnx + -1lnx = ln(6)

Reorder the terms:
5ln + -6ln + lnx + lnx + -1lnx = ln(6)

Combine like terms: 5ln + -6ln = -1ln
-1ln + lnx + lnx + -1lnx = ln(6)

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

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

Reorder the terms for easier multiplication:
-1ln + 1lnx = 6ln

Solving
-1ln + 1lnx = 6ln

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.
-1ln + -6ln + 1lnx = 6ln + -6ln

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

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

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-7 + x) = 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 + x)' equal to zero and attempt to solve:

Simplifying
-7 + x = 0

Solving
-7 + x = 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 + x = 0 + 7

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

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

Add '-1x' to each side of the equation.
x + -1x = 7 + -1x

Combine like terms: x + -1x = 0
0 = 7 + -1x

Simplifying
0 = 7 + -1x

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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