2*ln(x)=ln(2)+ln(x+12)

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


Simplifying
2ln(x) = ln(2) + ln(x + 12)

Multiply ln * x
2lnx = ln(2) + ln(x + 12)

Reorder the terms for easier multiplication:
2lnx = 2ln + ln(x + 12)

Reorder the terms:
2lnx = 2ln + ln(12 + x)
2lnx = 2ln + (12 * ln + x * ln)
2lnx = 2ln + (12ln + lnx)

Combine like terms: 2ln + 12ln = 14ln
2lnx = 14ln + lnx

Solving
2lnx = 14ln + lnx

Solving for variable 'l'.

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

Add '-14ln' to each side of the equation.
-14ln + 2lnx = 14ln + -14ln + lnx

Combine like terms: 14ln + -14ln = 0
-14ln + 2lnx = 0 + lnx
-14ln + 2lnx = lnx

Add '-1lnx' to each side of the equation.
-14ln + 2lnx + -1lnx = lnx + -1lnx

Combine like terms: 2lnx + -1lnx = 1lnx
-14ln + 1lnx = lnx + -1lnx

Combine like terms: lnx + -1lnx = 0
-14ln + 1lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-14 + 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 '(-14 + x)' equal to zero and attempt to solve:

Simplifying
-14 + x = 0

Solving
-14 + x = 0

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

Add '14' to each side of the equation.
-14 + 14 + x = 0 + 14

Combine like terms: -14 + 14 = 0
0 + x = 0 + 14
x = 0 + 14

Combine like terms: 0 + 14 = 14
x = 14

Add '-1x' to each side of the equation.
x + -1x = 14 + -1x

Combine like terms: x + -1x = 0
0 = 14 + -1x

Simplifying
0 = 14 + -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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