2lnx+3ln(1+x)-4ln(2x)=0

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Solution for 2lnx+3ln(1+x)-4ln(2x)=0 equation:


Simplifying
2lnx + 3ln(1 + x) + -4ln(2x) = 0
2lnx + (1 * 3ln + x * 3ln) + -4ln(2x) = 0
2lnx + (3ln + 3lnx) + -4ln(2x) = 0

Remove parenthesis around (2x)
2lnx + 3ln + 3lnx + -4ln * 2x = 0

Reorder the terms for easier multiplication:
2lnx + 3ln + 3lnx + -4 * 2ln * x = 0

Multiply -4 * 2
2lnx + 3ln + 3lnx + -8ln * x = 0

Multiply ln * x
2lnx + 3ln + 3lnx + -8lnx = 0

Reorder the terms:
3ln + 2lnx + 3lnx + -8lnx = 0

Combine like terms: 2lnx + 3lnx = 5lnx
3ln + 5lnx + -8lnx = 0

Combine like terms: 5lnx + -8lnx = -3lnx
3ln + -3lnx = 0

Solving
3ln + -3lnx = 0

Solving for variable 'l'.

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

Factor out the Greatest Common Factor (GCF), '3ln'.
3ln(1 + -1x) = 0

Ignore the factor 3.

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 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 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 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Add 'x' to each side of the equation. -1x + x = -1 + x Combine like terms: -1x + x = 0 0 = -1 + x Simplifying 0 = -1 + x 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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