2ln(x)=2ln(2)+ln(3-x)

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


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

Multiply ln * x
2lnx = 2ln(2) + ln(3 + -1x)

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

Multiply 2 * 2
2lnx = 4ln + ln(3 + -1x)
2lnx = 4ln + (3 * ln + -1x * ln)
2lnx = 4ln + (3ln + -1lnx)

Combine like terms: 4ln + 3ln = 7ln
2lnx = 7ln + -1lnx

Solving
2lnx = 7ln + -1lnx

Solving for variable 'l'.

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

Add '-7ln' to each side of the equation.
-7ln + 2lnx = 7ln + -7ln + -1lnx

Combine like terms: 7ln + -7ln = 0
-7ln + 2lnx = 0 + -1lnx
-7ln + 2lnx = -1lnx

Add 'lnx' to each side of the equation.
-7ln + 2lnx + lnx = -1lnx + lnx

Combine like terms: 2lnx + lnx = 3lnx
-7ln + 3lnx = -1lnx + lnx

Combine like terms: -1lnx + lnx = 0
-7ln + 3lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-7 + 3x) = 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 '(-7 + 3x)' equal to zero and attempt to solve:

Simplifying
-7 + 3x = 0

Solving
-7 + 3x = 0

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

Add '7' to each side of the equation.
-7 + 7 + 3x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + 3x = 0 + 7
3x = 0 + 7

Combine like terms: 0 + 7 = 7
3x = 7

Add '-3x' to each side of the equation.
3x + -3x = 7 + -3x

Combine like terms: 3x + -3x = 0
0 = 7 + -3x

Simplifying
0 = 7 + -3x

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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