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

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


Simplifying
ln(3x + -4) + -2ln(5x + -2) = -1ln(10x + -4)

Reorder the terms:
ln(-4 + 3x) + -2ln(5x + -2) = -1ln(10x + -4)
(-4 * ln + 3x * ln) + -2ln(5x + -2) = -1ln(10x + -4)
(-4ln + 3lnx) + -2ln(5x + -2) = -1ln(10x + -4)

Reorder the terms:
-4ln + 3lnx + -2ln(-2 + 5x) = -1ln(10x + -4)
-4ln + 3lnx + (-2 * -2ln + 5x * -2ln) = -1ln(10x + -4)
-4ln + 3lnx + (4ln + -10lnx) = -1ln(10x + -4)

Reorder the terms:
-4ln + 4ln + 3lnx + -10lnx = -1ln(10x + -4)

Combine like terms: -4ln + 4ln = 0
0 + 3lnx + -10lnx = -1ln(10x + -4)
3lnx + -10lnx = -1ln(10x + -4)

Combine like terms: 3lnx + -10lnx = -7lnx
-7lnx = -1ln(10x + -4)

Reorder the terms:
-7lnx = -1ln(-4 + 10x)
-7lnx = (-4 * -1ln + 10x * -1ln)
-7lnx = (4ln + -10lnx)

Solving
-7lnx = 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.
-4ln + -7lnx = 4ln + -4ln + -10lnx

Combine like terms: 4ln + -4ln = 0
-4ln + -7lnx = 0 + -10lnx
-4ln + -7lnx = -10lnx

Add '10lnx' to each side of the equation.
-4ln + -7lnx + 10lnx = -10lnx + 10lnx

Combine like terms: -7lnx + 10lnx = 3lnx
-4ln + 3lnx = -10lnx + 10lnx

Combine like terms: -10lnx + 10lnx = 0
-4ln + 3lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-4 + 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 '(-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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