ln(3x+6)-ln(x+5)=lnx

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Solution for ln(3x+6)-ln(x+5)=lnx equation: 


Simplifying
ln(3x + 6) + -1ln(x + 5) = lnx

Reorder the terms:
ln(6 + 3x) + -1ln(x + 5) = lnx
(6 * ln + 3x * ln) + -1ln(x + 5) = lnx
(6ln + 3lnx) + -1ln(x + 5) = lnx

Reorder the terms:
6ln + 3lnx + -1ln(5 + x) = lnx
6ln + 3lnx + (5 * -1ln + x * -1ln) = lnx
6ln + 3lnx + (-5ln + -1lnx) = lnx

Reorder the terms:
6ln + -5ln + 3lnx + -1lnx = lnx

Combine like terms: 6ln + -5ln = 1ln
1ln + 3lnx + -1lnx = lnx

Combine like terms: 3lnx + -1lnx = 2lnx
1ln + 2lnx = lnx

Solving
1ln + 2lnx = lnx

Solving for variable 'l'.

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

Add '-1lnx' to each side of the equation.
1ln + 2lnx + -1lnx = lnx + -1lnx

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

Combine like terms: lnx + -1lnx = 0
1ln + 1lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(1 + x) = 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 '(1 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

Solving
1 + x = 0

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

Add '-1' to each side of the equation.
1 + -1 + x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + x = 0 + -1
x = 0 + -1

Combine like terms: 0 + -1 = -1
x = -1

Add '-1x' to each side of the equation.
x + -1x = -1 + -1x

Combine like terms: x + -1x = 0
0 = -1 + -1x

Simplifying
0 = -1 + -1x

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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