ln(x+3)+ln(x-3)=ln(27)

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Solution for ln(x+3)+ln(x-3)=ln(27) equation: 


Simplifying
ln(x + 3) + ln(x + -3) = ln(27)

Reorder the terms:
ln(3 + x) + ln(x + -3) = ln(27)
(3 * ln + x * ln) + ln(x + -3) = ln(27)
(3ln + lnx) + ln(x + -3) = ln(27)

Reorder the terms:
3ln + lnx + ln(-3 + x) = ln(27)
3ln + lnx + (-3 * ln + x * ln) = ln(27)
3ln + lnx + (-3ln + lnx) = ln(27)

Reorder the terms:
3ln + -3ln + lnx + lnx = ln(27)

Combine like terms: 3ln + -3ln = 0
0 + lnx + lnx = ln(27)
lnx + lnx = ln(27)

Combine like terms: lnx + lnx = 2lnx
2lnx = ln(27)

Reorder the terms for easier multiplication:
2lnx = 27ln

Solving
2lnx = 27ln

Solving for variable 'l'.

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

Add '-27ln' to each side of the equation.
-27ln + 2lnx = 27ln + -27ln

Combine like terms: 27ln + -27ln = 0
-27ln + 2lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-27 + 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 '(-27 + 2x)' equal to zero and attempt to solve:

Simplifying
-27 + 2x = 0

Solving
-27 + 2x = 0

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

Add '27' to each side of the equation.
-27 + 27 + 2x = 0 + 27

Combine like terms: -27 + 27 = 0
0 + 2x = 0 + 27
2x = 0 + 27

Combine like terms: 0 + 27 = 27
2x = 27

Add '-2x' to each side of the equation.
2x + -2x = 27 + -2x

Combine like terms: 2x + -2x = 0
0 = 27 + -2x

Simplifying
0 = 27 + -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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