ln(x)+ln(x+6)=ln(27)

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Solution for ln(x)+ln(x+6)=ln(27) equation: 


Simplifying
ln(x) + ln(x + 6) = ln(27)

Multiply ln * x
lnx + ln(x + 6) = ln(27)

Reorder the terms:
lnx + ln(6 + x) = ln(27)
lnx + (6 * ln + x * ln) = ln(27)
lnx + (6ln + lnx) = ln(27)

Reorder the terms:
6ln + lnx + lnx = ln(27)

Combine like terms: lnx + lnx = 2lnx
6ln + 2lnx = ln(27)

Reorder the terms for easier multiplication:
6ln + 2lnx = 27ln

Solving
6ln + 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.
6ln + -27ln + 2lnx = 27ln + -27ln

Combine like terms: 6ln + -27ln = -21ln
-21ln + 2lnx = 27ln + -27ln

Combine like terms: 27ln + -27ln = 0
-21ln + 2lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-21 + 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 '(-21 + 2x)' equal to zero and attempt to solve:

Simplifying
-21 + 2x = 0

Solving
-21 + 2x = 0

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

Add '21' to each side of the equation.
-21 + 21 + 2x = 0 + 21

Combine like terms: -21 + 21 = 0
0 + 2x = 0 + 21
2x = 0 + 21

Combine like terms: 0 + 21 = 21
2x = 21

Add '-2x' to each side of the equation.
2x + -2x = 21 + -2x

Combine like terms: 2x + -2x = 0
0 = 21 + -2x

Simplifying
0 = 21 + -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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