ln(x)+ln(x-6)=ln(5x-28)

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Solution for ln(x)+ln(x-6)=ln(5x-28) equation:


Simplifying
ln(x) + ln(x + -6) = ln(5x + -28)

Multiply ln * x
lnx + ln(x + -6) = ln(5x + -28)

Reorder the terms:
lnx + ln(-6 + x) = ln(5x + -28)
lnx + (-6 * ln + x * ln) = ln(5x + -28)
lnx + (-6ln + lnx) = ln(5x + -28)

Reorder the terms:
-6ln + lnx + lnx = ln(5x + -28)

Combine like terms: lnx + lnx = 2lnx
-6ln + 2lnx = ln(5x + -28)

Reorder the terms:
-6ln + 2lnx = ln(-28 + 5x)
-6ln + 2lnx = (-28 * ln + 5x * ln)
-6ln + 2lnx = (-28ln + 5lnx)

Solving
-6ln + 2lnx = -28ln + 5lnx

Solving for variable 'l'.

Move all terms containing l to the left, all other terms to the right.

Add '28ln' to each side of the equation.
-6ln + 28ln + 2lnx = -28ln + 28ln + 5lnx

Combine like terms: -6ln + 28ln = 22ln
22ln + 2lnx = -28ln + 28ln + 5lnx

Combine like terms: -28ln + 28ln = 0
22ln + 2lnx = 0 + 5lnx
22ln + 2lnx = 5lnx

Add '-5lnx' to each side of the equation.
22ln + 2lnx + -5lnx = 5lnx + -5lnx

Combine like terms: 2lnx + -5lnx = -3lnx
22ln + -3lnx = 5lnx + -5lnx

Combine like terms: 5lnx + -5lnx = 0
22ln + -3lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(22 + -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 '(22 + -3x)' equal to zero and attempt to solve: Simplifying 22 + -3x = 0 Solving 22 + -3x = 0 Move all terms containing l to the left, all other terms to the right. Add '-22' to each side of the equation. 22 + -22 + -3x = 0 + -22 Combine like terms: 22 + -22 = 0 0 + -3x = 0 + -22 -3x = 0 + -22 Combine like terms: 0 + -22 = -22 -3x = -22 Add '3x' to each side of the equation. -3x + 3x = -22 + 3x Combine like terms: -3x + 3x = 0 0 = -22 + 3x Simplifying 0 = -22 + 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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