ln(4x^2-3x)=ln(8x-6)-ln(2x)

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Solution for ln(4x^2-3x)=ln(8x-6)-ln(2x) equation:


Simplifying
ln(4x2 + -3x) = ln(8x + -6) + -1ln(2x)

Reorder the terms:
ln(-3x + 4x2) = ln(8x + -6) + -1ln(2x)
(-3x * ln + 4x2 * ln) = ln(8x + -6) + -1ln(2x)
(-3lnx + 4lnx2) = ln(8x + -6) + -1ln(2x)

Reorder the terms:
-3lnx + 4lnx2 = ln(-6 + 8x) + -1ln(2x)
-3lnx + 4lnx2 = (-6 * ln + 8x * ln) + -1ln(2x)
-3lnx + 4lnx2 = (-6ln + 8lnx) + -1ln(2x)

Remove parenthesis around (2x)
-3lnx + 4lnx2 = -6ln + 8lnx + -1ln * 2x

Reorder the terms for easier multiplication:
-3lnx + 4lnx2 = -6ln + 8lnx + -1 * 2ln * x

Multiply -1 * 2
-3lnx + 4lnx2 = -6ln + 8lnx + -2ln * x

Multiply ln * x
-3lnx + 4lnx2 = -6ln + 8lnx + -2lnx

Combine like terms: 8lnx + -2lnx = 6lnx
-3lnx + 4lnx2 = -6ln + 6lnx

Solving
-3lnx + 4lnx2 = -6ln + 6lnx

Solving for variable 'l'.

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

Add '6ln' to each side of the equation.
-3lnx + 6ln + 4lnx2 = -6ln + 6ln + 6lnx

Reorder the terms:
6ln + -3lnx + 4lnx2 = -6ln + 6ln + 6lnx

Combine like terms: -6ln + 6ln = 0
6ln + -3lnx + 4lnx2 = 0 + 6lnx
6ln + -3lnx + 4lnx2 = 6lnx

Add '-6lnx' to each side of the equation.
6ln + -3lnx + -6lnx + 4lnx2 = 6lnx + -6lnx

Combine like terms: -3lnx + -6lnx = -9lnx
6ln + -9lnx + 4lnx2 = 6lnx + -6lnx

Combine like terms: 6lnx + -6lnx = 0
6ln + -9lnx + 4lnx2 = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(6 + -9x + 4x2) = 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 '(6 + -9x + 4x2)' equal to zero and attempt to solve: Simplifying 6 + -9x + 4x2 = 0 Solving 6 + -9x + 4x2 = 0 Move all terms containing l to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -9x + -6 + 4x2 = 0 + -6 Reorder the terms: 6 + -6 + -9x + 4x2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -9x + 4x2 = 0 + -6 -9x + 4x2 = 0 + -6 Combine like terms: 0 + -6 = -6 -9x + 4x2 = -6 Add '9x' to each side of the equation. -9x + 9x + 4x2 = -6 + 9x Combine like terms: -9x + 9x = 0 0 + 4x2 = -6 + 9x 4x2 = -6 + 9x Add '-4x2' to each side of the equation. 4x2 + -4x2 = -6 + 9x + -4x2 Combine like terms: 4x2 + -4x2 = 0 0 = -6 + 9x + -4x2 Simplifying 0 = -6 + 9x + -4x2 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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