2*ln*x+ln*(x+1)=ln*6*x

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Solution for 2*ln*x+ln*(x+1)=ln*6*x equation:


Simplifying
2ln * x + ln(x + 1) = ln * 6x

Multiply ln * x
2lnx + ln(x + 1) = ln * 6x

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

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

Combine like terms: 2lnx + lnx = 3lnx
1ln + 3lnx = ln * 6x

Reorder the terms for easier multiplication:
1ln + 3lnx = 6ln * x

Multiply ln * x
1ln + 3lnx = 6lnx

Solving
1ln + 3lnx = 6lnx

Solving for variable 'l'.

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

Add '-6lnx' to each side of the equation.
1ln + 3lnx + -6lnx = 6lnx + -6lnx

Combine like terms: 3lnx + -6lnx = -3lnx
1ln + -3lnx = 6lnx + -6lnx

Combine like terms: 6lnx + -6lnx = 0
1ln + -3lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(1 + -3x) = 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 '(1 + -3x)' equal to zero and attempt to solve: Simplifying 1 + -3x = 0 Solving 1 + -3x = 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 + -3x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3x = 0 + -1 -3x = 0 + -1 Combine like terms: 0 + -1 = -1 -3x = -1 Add '3x' to each side of the equation. -3x + 3x = -1 + 3x Combine like terms: -3x + 3x = 0 0 = -1 + 3x Simplifying 0 = -1 + 3x 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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