ln(x+2)+ln(x-1)=ln(6)

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Solution for ln(x+2)+ln(x-1)=ln(6) equation: 


Simplifying
ln(x + 2) + ln(x + -1) = ln(6)

Reorder the terms:
ln(2 + x) + ln(x + -1) = ln(6)
(2 * ln + x * ln) + ln(x + -1) = ln(6)
(2ln + lnx) + ln(x + -1) = ln(6)

Reorder the terms:
2ln + lnx + ln(-1 + x) = ln(6)
2ln + lnx + (-1 * ln + x * ln) = ln(6)
2ln + lnx + (-1ln + lnx) = ln(6)

Reorder the terms:
2ln + -1ln + lnx + lnx = ln(6)

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

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

Reorder the terms for easier multiplication:
1ln + 2lnx = 6ln

Solving
1ln + 2lnx = 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 + 2lnx = 6ln + -6ln

Combine like terms: 1ln + -6ln = -5ln
-5ln + 2lnx = 6ln + -6ln

Combine like terms: 6ln + -6ln = 0
-5ln + 2lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-5 + 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 '(-5 + 2x)' equal to zero and attempt to solve:

Simplifying
-5 + 2x = 0

Solving
-5 + 2x = 0

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

Add '5' to each side of the equation.
-5 + 5 + 2x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + 2x = 0 + 5
2x = 0 + 5

Combine like terms: 0 + 5 = 5
2x = 5

Add '-2x' to each side of the equation.
2x + -2x = 5 + -2x

Combine like terms: 2x + -2x = 0
0 = 5 + -2x

Simplifying
0 = 5 + -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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