ln(x-3)+ln(x+6)=ln(22)

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Solution for ln(x-3)+ln(x+6)=ln(22) equation: 


Simplifying
ln(x + -3) + ln(x + 6) = ln(22)

Reorder the terms:
ln(-3 + x) + ln(x + 6) = ln(22)
(-3 * ln + x * ln) + ln(x + 6) = ln(22)
(-3ln + lnx) + ln(x + 6) = ln(22)

Reorder the terms:
-3ln + lnx + ln(6 + x) = ln(22)
-3ln + lnx + (6 * ln + x * ln) = ln(22)
-3ln + lnx + (6ln + lnx) = ln(22)

Reorder the terms:
-3ln + 6ln + lnx + lnx = ln(22)

Combine like terms: -3ln + 6ln = 3ln
3ln + lnx + lnx = ln(22)

Combine like terms: lnx + lnx = 2lnx
3ln + 2lnx = ln(22)

Reorder the terms for easier multiplication:
3ln + 2lnx = 22ln

Solving
3ln + 2lnx = 22ln

Solving for variable 'l'.

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

Add '-22ln' to each side of the equation.
3ln + -22ln + 2lnx = 22ln + -22ln

Combine like terms: 3ln + -22ln = -19ln
-19ln + 2lnx = 22ln + -22ln

Combine like terms: 22ln + -22ln = 0
-19ln + 2lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-19 + 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 '(-19 + 2x)' equal to zero and attempt to solve:

Simplifying
-19 + 2x = 0

Solving
-19 + 2x = 0

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

Add '19' to each side of the equation.
-19 + 19 + 2x = 0 + 19

Combine like terms: -19 + 19 = 0
0 + 2x = 0 + 19
2x = 0 + 19

Combine like terms: 0 + 19 = 19
2x = 19

Add '-2x' to each side of the equation.
2x + -2x = 19 + -2x

Combine like terms: 2x + -2x = 0
0 = 19 + -2x

Simplifying
0 = 19 + -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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