2lnx-ln(2x-7)=ln(9x)-ln(x-2)

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Solution for 2lnx-ln(2x-7)=ln(9x)-ln(x-2) equation:


Simplifying
2lnx + -1ln(2x + -7) = ln(9x) + -1ln(x + -2)

Reorder the terms:
2lnx + -1ln(-7 + 2x) = ln(9x) + -1ln(x + -2)
2lnx + (-7 * -1ln + 2x * -1ln) = ln(9x) + -1ln(x + -2)
2lnx + (7ln + -2lnx) = ln(9x) + -1ln(x + -2)

Reorder the terms:
7ln + 2lnx + -2lnx = ln(9x) + -1ln(x + -2)

Combine like terms: 2lnx + -2lnx = 0
7ln + 0 = ln(9x) + -1ln(x + -2)
7ln = ln(9x) + -1ln(x + -2)

Remove parenthesis around (9x)
7ln = ln * 9x + -1ln(x + -2)

Reorder the terms for easier multiplication:
7ln = 9ln * x + -1ln(x + -2)

Multiply ln * x
7ln = 9lnx + -1ln(x + -2)

Reorder the terms:
7ln = 9lnx + -1ln(-2 + x)
7ln = 9lnx + (-2 * -1ln + x * -1ln)
7ln = 9lnx + (2ln + -1lnx)

Reorder the terms:
7ln = 2ln + 9lnx + -1lnx

Combine like terms: 9lnx + -1lnx = 8lnx
7ln = 2ln + 8lnx

Solving
7ln = 2ln + 8lnx

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.
7ln + -2ln = 2ln + -2ln + 8lnx

Combine like terms: 7ln + -2ln = 5ln
5ln = 2ln + -2ln + 8lnx

Combine like terms: 2ln + -2ln = 0
5ln = 0 + 8lnx
5ln = 8lnx

Add '-8lnx' to each side of the equation.
5ln + -8lnx = 8lnx + -8lnx

Combine like terms: 8lnx + -8lnx = 0
5ln + -8lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(5 + -8x) = 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 '(5 + -8x)' equal to zero and attempt to solve: Simplifying 5 + -8x = 0 Solving 5 + -8x = 0 Move all terms containing l to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -8x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -8x = 0 + -5 -8x = 0 + -5 Combine like terms: 0 + -5 = -5 -8x = -5 Add '8x' to each side of the equation. -8x + 8x = -5 + 8x Combine like terms: -8x + 8x = 0 0 = -5 + 8x Simplifying 0 = -5 + 8x 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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