ln(x-1)=ln(5x-7)-ln(x-1)

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Solution for ln(x-1)=ln(5x-7)-ln(x-1) equation:


Simplifying
ln(x + -1) = ln(5x + -7) + -1ln(x + -1)

Reorder the terms:
ln(-1 + x) = ln(5x + -7) + -1ln(x + -1)
(-1 * ln + x * ln) = ln(5x + -7) + -1ln(x + -1)
(-1ln + lnx) = ln(5x + -7) + -1ln(x + -1)

Reorder the terms:
-1ln + lnx = ln(-7 + 5x) + -1ln(x + -1)
-1ln + lnx = (-7 * ln + 5x * ln) + -1ln(x + -1)
-1ln + lnx = (-7ln + 5lnx) + -1ln(x + -1)

Reorder the terms:
-1ln + lnx = -7ln + 5lnx + -1ln(-1 + x)
-1ln + lnx = -7ln + 5lnx + (-1 * -1ln + x * -1ln)
-1ln + lnx = -7ln + 5lnx + (1ln + -1lnx)

Reorder the terms:
-1ln + lnx = -7ln + 1ln + 5lnx + -1lnx

Combine like terms: -7ln + 1ln = -6ln
-1ln + lnx = -6ln + 5lnx + -1lnx

Combine like terms: 5lnx + -1lnx = 4lnx
-1ln + lnx = -6ln + 4lnx

Solving
-1ln + lnx = -6ln + 4lnx

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.
-1ln + 6ln + lnx = -6ln + 6ln + 4lnx

Combine like terms: -1ln + 6ln = 5ln
5ln + lnx = -6ln + 6ln + 4lnx

Combine like terms: -6ln + 6ln = 0
5ln + lnx = 0 + 4lnx
5ln + lnx = 4lnx

Add '-4lnx' to each side of the equation.
5ln + lnx + -4lnx = 4lnx + -4lnx

Combine like terms: lnx + -4lnx = -3lnx
5ln + -3lnx = 4lnx + -4lnx

Combine like terms: 4lnx + -4lnx = 0
5ln + -3lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(5 + -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 '(5 + -3x)' equal to zero and attempt to solve: Simplifying 5 + -3x = 0 Solving 5 + -3x = 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 + -3x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3x = 0 + -5 -3x = 0 + -5 Combine like terms: 0 + -5 = -5 -3x = -5 Add '3x' to each side of the equation. -3x + 3x = -5 + 3x Combine like terms: -3x + 3x = 0 0 = -5 + 3x Simplifying 0 = -5 + 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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