2lnx=ln(4x+6)-ln(2)

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Solution for 2lnx=ln(4x+6)-ln(2) equation:


Simplifying
2lnx = ln(4x + 6) + -1ln(2)

Reorder the terms:
2lnx = ln(6 + 4x) + -1ln(2)
2lnx = (6 * ln + 4x * ln) + -1ln(2)
2lnx = (6ln + 4lnx) + -1ln(2)

Reorder the terms for easier multiplication:
2lnx = 6ln + 4lnx + -1 * 2ln

Multiply -1 * 2
2lnx = 6ln + 4lnx + -2ln

Reorder the terms:
2lnx = 6ln + -2ln + 4lnx

Combine like terms: 6ln + -2ln = 4ln
2lnx = 4ln + 4lnx

Solving
2lnx = 4ln + 4lnx

Solving for variable 'l'.

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

Add '-4ln' to each side of the equation.
-4ln + 2lnx = 4ln + -4ln + 4lnx

Combine like terms: 4ln + -4ln = 0
-4ln + 2lnx = 0 + 4lnx
-4ln + 2lnx = 4lnx

Add '-4lnx' to each side of the equation.
-4ln + 2lnx + -4lnx = 4lnx + -4lnx

Combine like terms: 2lnx + -4lnx = -2lnx
-4ln + -2lnx = 4lnx + -4lnx

Combine like terms: 4lnx + -4lnx = 0
-4ln + -2lnx = 0

Factor out the Greatest Common Factor (GCF), '-2ln'.
-2ln(2 + x) = 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 '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Add '-1x' to each side of the equation. x + -1x = -2 + -1x Combine like terms: x + -1x = 0 0 = -2 + -1x Simplifying 0 = -2 + -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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