2ln(2x+1)=lnx^2

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Solution for 2ln(2x+1)=lnx^2 equation:


Simplifying
2ln(2x + 1) = lnx2

Reorder the terms:
2ln(1 + 2x) = lnx2
(1 * 2ln + 2x * 2ln) = lnx2
(2ln + 4lnx) = lnx2

Solving
2ln + 4lnx = lnx2

Solving for variable 'l'.

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

Add '-1lnx2' to each side of the equation.
2ln + 4lnx + -1lnx2 = lnx2 + -1lnx2

Combine like terms: lnx2 + -1lnx2 = 0
2ln + 4lnx + -1lnx2 = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(2 + 4x + -1x2) = 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 '(2 + 4x + -1x2)' equal to zero and attempt to solve: Simplifying 2 + 4x + -1x2 = 0 Solving 2 + 4x + -1x2 = 0 Move all terms containing l to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + 4x + -2 + -1x2 = 0 + -2 Reorder the terms: 2 + -2 + 4x + -1x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 4x + -1x2 = 0 + -2 4x + -1x2 = 0 + -2 Combine like terms: 0 + -2 = -2 4x + -1x2 = -2 Add '-4x' to each side of the equation. 4x + -4x + -1x2 = -2 + -4x Combine like terms: 4x + -4x = 0 0 + -1x2 = -2 + -4x -1x2 = -2 + -4x Add 'x2' to each side of the equation. -1x2 + x2 = -2 + -4x + x2 Combine like terms: -1x2 + x2 = 0 0 = -2 + -4x + x2 Simplifying 0 = -2 + -4x + x2 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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