ln(x-1)+ln(x-6)=ln(5)

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Solution for ln(x-1)+ln(x-6)=ln(5) equation:


Simplifying
ln(x + -1) + ln(x + -6) = ln(5)

Reorder the terms:
ln(-1 + x) + ln(x + -6) = ln(5)
(-1 * ln + x * ln) + ln(x + -6) = ln(5)
(-1ln + lnx) + ln(x + -6) = ln(5)

Reorder the terms:
-1ln + lnx + ln(-6 + x) = ln(5)
-1ln + lnx + (-6 * ln + x * ln) = ln(5)
-1ln + lnx + (-6ln + lnx) = ln(5)

Reorder the terms:
-1ln + -6ln + lnx + lnx = ln(5)

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

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

Reorder the terms for easier multiplication:
-7ln + 2lnx = 5ln

Solving
-7ln + 2lnx = 5ln

Solving for variable 'l'.

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

Add '-5ln' to each side of the equation.
-7ln + -5ln + 2lnx = 5ln + -5ln

Combine like terms: -7ln + -5ln = -12ln
-12ln + 2lnx = 5ln + -5ln

Combine like terms: 5ln + -5ln = 0
-12ln + 2lnx = 0

Factor out the Greatest Common Factor (GCF), '2ln'.
2ln(-6 + x) = 0

Ignore the factor 2.

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 '(-6 + x)' equal to zero and attempt to solve: Simplifying -6 + x = 0 Solving -6 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 0 + 6 Combine like terms: -6 + 6 = 0 0 + x = 0 + 6 x = 0 + 6 Combine like terms: 0 + 6 = 6 x = 6 Add '-1x' to each side of the equation. x + -1x = 6 + -1x Combine like terms: x + -1x = 0 0 = 6 + -1x Simplifying 0 = 6 + -1x 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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