2ln(x)-ln(3x-8)=ln(5x)-ln(x+2)

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Solution for 2ln(x)-ln(3x-8)=ln(5x)-ln(x+2) equation:


Simplifying
2ln(x) + -1ln(3x + -8) = ln(5x) + -1ln(x + 2)

Multiply ln * x
2lnx + -1ln(3x + -8) = ln(5x) + -1ln(x + 2)

Reorder the terms:
2lnx + -1ln(-8 + 3x) = ln(5x) + -1ln(x + 2)
2lnx + (-8 * -1ln + 3x * -1ln) = ln(5x) + -1ln(x + 2)
2lnx + (8ln + -3lnx) = ln(5x) + -1ln(x + 2)

Reorder the terms:
8ln + 2lnx + -3lnx = ln(5x) + -1ln(x + 2)

Combine like terms: 2lnx + -3lnx = -1lnx
8ln + -1lnx = ln(5x) + -1ln(x + 2)

Remove parenthesis around (5x)
8ln + -1lnx = ln * 5x + -1ln(x + 2)

Reorder the terms for easier multiplication:
8ln + -1lnx = 5ln * x + -1ln(x + 2)

Multiply ln * x
8ln + -1lnx = 5lnx + -1ln(x + 2)

Reorder the terms:
8ln + -1lnx = 5lnx + -1ln(2 + x)
8ln + -1lnx = 5lnx + (2 * -1ln + x * -1ln)
8ln + -1lnx = 5lnx + (-2ln + -1lnx)

Reorder the terms:
8ln + -1lnx = -2ln + 5lnx + -1lnx

Combine like terms: 5lnx + -1lnx = 4lnx
8ln + -1lnx = -2ln + 4lnx

Solving
8ln + -1lnx = -2ln + 4lnx

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.
8ln + 2ln + -1lnx = -2ln + 2ln + 4lnx

Combine like terms: 8ln + 2ln = 10ln
10ln + -1lnx = -2ln + 2ln + 4lnx

Combine like terms: -2ln + 2ln = 0
10ln + -1lnx = 0 + 4lnx
10ln + -1lnx = 4lnx

Add '-4lnx' to each side of the equation.
10ln + -1lnx + -4lnx = 4lnx + -4lnx

Combine like terms: -1lnx + -4lnx = -5lnx
10ln + -5lnx = 4lnx + -4lnx

Combine like terms: 4lnx + -4lnx = 0
10ln + -5lnx = 0

Factor out the Greatest Common Factor (GCF), '5ln'.
5ln(2 + -1x) = 0

Ignore the factor 5.

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 '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 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 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Add 'x' to each side of the equation. -1x + x = -2 + x Combine like terms: -1x + x = 0 0 = -2 + x Simplifying 0 = -2 + x 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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