2ln(x)=ln(15)+2ln(2)-ln(12)

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Solution for 2ln(x)=ln(15)+2ln(2)-ln(12) equation: 


Simplifying
2ln(x) = ln(15) + 2ln(2) + -1ln(12)

Multiply ln * x
2lnx = ln(15) + 2ln(2) + -1ln(12)

Reorder the terms for easier multiplication:
2lnx = 15ln + 2ln(2) + -1ln(12)

Reorder the terms for easier multiplication:
2lnx = 15ln + 2 * 2ln + -1ln(12)

Multiply 2 * 2
2lnx = 15ln + 4ln + -1ln(12)

Reorder the terms for easier multiplication:
2lnx = 15ln + 4ln + -1 * 12ln

Multiply -1 * 12
2lnx = 15ln + 4ln + -12ln

Combine like terms: 15ln + 4ln = 19ln
2lnx = 19ln + -12ln

Combine like terms: 19ln + -12ln = 7ln
2lnx = 7ln

Solving
2lnx = 7ln

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

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

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-7 + 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 '(-7 + 2x)' equal to zero and attempt to solve:

Simplifying
-7 + 2x = 0

Solving
-7 + 2x = 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 + 2x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + 2x = 0 + 7
2x = 0 + 7

Combine like terms: 0 + 7 = 7
2x = 7

Add '-2x' to each side of the equation.
2x + -2x = 7 + -2x

Combine like terms: 2x + -2x = 0
0 = 7 + -2x

Simplifying
0 = 7 + -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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