2lnx=ln(7x-12)

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Solution for 2lnx=ln(7x-12) equation: 


Simplifying
2lnx = ln(7x + -12)

Reorder the terms:
2lnx = ln(-12 + 7x)
2lnx = (-12 * ln + 7x * ln)
2lnx = (-12ln + 7lnx)

Solving
2lnx = -12ln + 7lnx

Solving for variable 'l'.

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

Add '12ln' to each side of the equation.
12ln + 2lnx = -12ln + 12ln + 7lnx

Combine like terms: -12ln + 12ln = 0
12ln + 2lnx = 0 + 7lnx
12ln + 2lnx = 7lnx

Add '-7lnx' to each side of the equation.
12ln + 2lnx + -7lnx = 7lnx + -7lnx

Combine like terms: 2lnx + -7lnx = -5lnx
12ln + -5lnx = 7lnx + -7lnx

Combine like terms: 7lnx + -7lnx = 0
12ln + -5lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(12 + -5x) = 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 '(12 + -5x)' equal to zero and attempt to solve:

Simplifying
12 + -5x = 0

Solving
12 + -5x = 0

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

Add '-12' to each side of the equation.
12 + -12 + -5x = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -5x = 0 + -12
-5x = 0 + -12

Combine like terms: 0 + -12 = -12
-5x = -12

Add '5x' to each side of the equation.
-5x + 5x = -12 + 5x

Combine like terms: -5x + 5x = 0
0 = -12 + 5x

Simplifying
0 = -12 + 5x

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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