ln(6x)-ln(x-1)=ln(4)

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Solution for ln(6x)-ln(x-1)=ln(4) equation:


Simplifying
ln(6x) + -1ln(x + -1) = ln(4)

Remove parenthesis around (6x)
ln * 6x + -1ln(x + -1) = ln(4)

Reorder the terms for easier multiplication:
6ln * x + -1ln(x + -1) = ln(4)

Multiply ln * x
6lnx + -1ln(x + -1) = ln(4)

Reorder the terms:
6lnx + -1ln(-1 + x) = ln(4)
6lnx + (-1 * -1ln + x * -1ln) = ln(4)
6lnx + (1ln + -1lnx) = ln(4)

Reorder the terms:
1ln + 6lnx + -1lnx = ln(4)

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

Reorder the terms for easier multiplication:
1ln + 5lnx = 4ln

Solving
1ln + 5lnx = 4ln

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.
1ln + -4ln + 5lnx = 4ln + -4ln

Combine like terms: 1ln + -4ln = -3ln
-3ln + 5lnx = 4ln + -4ln

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

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