2ln(3x-4)+ln(10x-4)=2ln(5x-2)

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Solution for 2ln(3x-4)+ln(10x-4)=2ln(5x-2) equation:


Simplifying
2ln(3x + -4) + ln(10x + -4) = 2ln(5x + -2)

Reorder the terms:
2ln(-4 + 3x) + ln(10x + -4) = 2ln(5x + -2)
(-4 * 2ln + 3x * 2ln) + ln(10x + -4) = 2ln(5x + -2)
(-8ln + 6lnx) + ln(10x + -4) = 2ln(5x + -2)

Reorder the terms:
-8ln + 6lnx + ln(-4 + 10x) = 2ln(5x + -2)
-8ln + 6lnx + (-4 * ln + 10x * ln) = 2ln(5x + -2)
-8ln + 6lnx + (-4ln + 10lnx) = 2ln(5x + -2)

Reorder the terms:
-8ln + -4ln + 6lnx + 10lnx = 2ln(5x + -2)

Combine like terms: -8ln + -4ln = -12ln
-12ln + 6lnx + 10lnx = 2ln(5x + -2)

Combine like terms: 6lnx + 10lnx = 16lnx
-12ln + 16lnx = 2ln(5x + -2)

Reorder the terms:
-12ln + 16lnx = 2ln(-2 + 5x)
-12ln + 16lnx = (-2 * 2ln + 5x * 2ln)
-12ln + 16lnx = (-4ln + 10lnx)

Solving
-12ln + 16lnx = -4ln + 10lnx

Solving for variable 'l'.

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

Add '4ln' to each side of the equation.
-12ln + 4ln + 16lnx = -4ln + 4ln + 10lnx

Combine like terms: -12ln + 4ln = -8ln
-8ln + 16lnx = -4ln + 4ln + 10lnx

Combine like terms: -4ln + 4ln = 0
-8ln + 16lnx = 0 + 10lnx
-8ln + 16lnx = 10lnx

Add '-10lnx' to each side of the equation.
-8ln + 16lnx + -10lnx = 10lnx + -10lnx

Combine like terms: 16lnx + -10lnx = 6lnx
-8ln + 6lnx = 10lnx + -10lnx

Combine like terms: 10lnx + -10lnx = 0
-8ln + 6lnx = 0

Factor out the Greatest Common Factor (GCF), '2ln'.
2ln(-4 + 3x) = 0

Ignore the factor 2.

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 '(-4 + 3x)' equal to zero and attempt to solve: Simplifying -4 + 3x = 0 Solving -4 + 3x = 0 Move all terms containing l to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + 3x = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 3x = 0 + 4 3x = 0 + 4 Combine like terms: 0 + 4 = 4 3x = 4 Add '-3x' to each side of the equation. 3x + -3x = 4 + -3x Combine like terms: 3x + -3x = 0 0 = 4 + -3x Simplifying 0 = 4 + -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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