ln(6x-1)(x)=ln(2)

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


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

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

Reorder the terms for easier multiplication:
ln * x(-1 + 6x) = ln(2)

Multiply ln * x
lnx(-1 + 6x) = ln(2)
(-1 * lnx + 6x * lnx) = ln(2)
(-1lnx + 6lnx2) = ln(2)

Reorder the terms for easier multiplication:
-1lnx + 6lnx2 = 2ln

Solving
-1lnx + 6lnx2 = 2ln

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.
-1lnx + -2ln + 6lnx2 = 2ln + -2ln

Reorder the terms:
-2ln + -1lnx + 6lnx2 = 2ln + -2ln

Combine like terms: 2ln + -2ln = 0
-2ln + -1lnx + 6lnx2 = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-2 + -1x + 6x2) = 0

Factor a trinomial.
ln((-1 + -2x)(2 + -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 + -2x)' equal to zero and attempt to solve: Simplifying -1 + -2x = 0 Solving -1 + -2x = 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 + -2x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2x = 0 + 1 -2x = 0 + 1 Combine like terms: 0 + 1 = 1 -2x = 1 Add '2x' to each side of the equation. -2x + 2x = 1 + 2x Combine like terms: -2x + 2x = 0 0 = 1 + 2x Simplifying 0 = 1 + 2x The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.

Subproblem 3

Set the factor '(2 + -3x)' equal to zero and attempt to solve: Simplifying 2 + -3x = 0 Solving 2 + -3x = 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 + -3x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3x = 0 + -2 -3x = 0 + -2 Combine like terms: 0 + -2 = -2 -3x = -2 Add '3x' to each side of the equation. -3x + 3x = -2 + 3x Combine like terms: -3x + 3x = 0 0 = -2 + 3x Simplifying 0 = -2 + 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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