ln(x+2)+ln(x-7)=ln(6)

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Solution for ln(x+2)+ln(x-7)=ln(6) equation: 


Simplifying
ln(x + 2) + ln(x + -7) = ln(6)

Reorder the terms:
ln(2 + x) + ln(x + -7) = ln(6)
(2 * ln + x * ln) + ln(x + -7) = ln(6)
(2ln + lnx) + ln(x + -7) = ln(6)

Reorder the terms:
2ln + lnx + ln(-7 + x) = ln(6)
2ln + lnx + (-7 * ln + x * ln) = ln(6)
2ln + lnx + (-7ln + lnx) = ln(6)

Reorder the terms:
2ln + -7ln + lnx + lnx = ln(6)

Combine like terms: 2ln + -7ln = -5ln
-5ln + lnx + lnx = ln(6)

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

Reorder the terms for easier multiplication:
-5ln + 2lnx = 6ln

Solving
-5ln + 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.
-5ln + -6ln + 2lnx = 6ln + -6ln

Combine like terms: -5ln + -6ln = -11ln
-11ln + 2lnx = 6ln + -6ln

Combine like terms: 6ln + -6ln = 0
-11ln + 2lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-11 + 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 '(-11 + 2x)' equal to zero and attempt to solve:

Simplifying
-11 + 2x = 0

Solving
-11 + 2x = 0

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

Add '11' to each side of the equation.
-11 + 11 + 2x = 0 + 11

Combine like terms: -11 + 11 = 0
0 + 2x = 0 + 11
2x = 0 + 11

Combine like terms: 0 + 11 = 11
2x = 11

Add '-2x' to each side of the equation.
2x + -2x = 11 + -2x

Combine like terms: 2x + -2x = 0
0 = 11 + -2x

Simplifying
0 = 11 + -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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