ln(x+3)-lnx=2lnx

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Solution for ln(x+3)-lnx=2lnx equation: 


Simplifying
ln(x + 3) + -1lnx = 2lnx

Reorder the terms:
ln(3 + x) + -1lnx = 2lnx
(3 * ln + x * ln) + -1lnx = 2lnx
(3ln + lnx) + -1lnx = 2lnx

Combine like terms: lnx + -1lnx = 0
3ln + 0 = 2lnx
3ln = 2lnx

Solving
3ln = 2lnx

Solving for variable 'l'.

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

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

Combine like terms: 2lnx + -2lnx = 0
3ln + -2lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(3 + -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 '(3 + -2x)' equal to zero and attempt to solve:

Simplifying
3 + -2x = 0

Solving
3 + -2x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2x = 0 + -3
-2x = 0 + -3

Combine like terms: 0 + -3 = -3
-2x = -3

Add '2x' to each side of the equation.
-2x + 2x = -3 + 2x

Combine like terms: -2x + 2x = 0
0 = -3 + 2x

Simplifying
0 = -3 + 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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