2lnx=-ln(6x+2)

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Solution for 2lnx=-ln(6x+2) equation:


Simplifying
2lnx = -1ln(6x + 2)

Reorder the terms:
2lnx = -1ln(2 + 6x)
2lnx = (2 * -1ln + 6x * -1ln)
2lnx = (-2ln + -6lnx)

Solving
2lnx = -2ln + -6lnx

Solving for variable 'l'.

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

Add '2ln' to each side of the equation.
2ln + 2lnx = -2ln + 2ln + -6lnx

Combine like terms: -2ln + 2ln = 0
2ln + 2lnx = 0 + -6lnx
2ln + 2lnx = -6lnx

Add '6lnx' to each side of the equation.
2ln + 2lnx + 6lnx = -6lnx + 6lnx

Combine like terms: 2lnx + 6lnx = 8lnx
2ln + 8lnx = -6lnx + 6lnx

Combine like terms: -6lnx + 6lnx = 0
2ln + 8lnx = 0

Factor out the Greatest Common Factor (GCF), '2ln'.
2ln(1 + 4x) = 0

Ignore the factor 2.

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 '(1 + 4x)' equal to zero and attempt to solve: Simplifying 1 + 4x = 0 Solving 1 + 4x = 0 Move all terms containing l to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 4x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 4x = 0 + -1 4x = 0 + -1 Combine like terms: 0 + -1 = -1 4x = -1 Add '-4x' to each side of the equation. 4x + -4x = -1 + -4x Combine like terms: 4x + -4x = 0 0 = -1 + -4x Simplifying 0 = -1 + -4x 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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