ln(x)+ln(x-2)=ln(120)

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Solution for ln(x)+ln(x-2)=ln(120) equation:


Simplifying
ln(x) + ln(x + -2) = ln(120)

Multiply ln * x
lnx + ln(x + -2) = ln(120)

Reorder the terms:
lnx + ln(-2 + x) = ln(120)
lnx + (-2 * ln + x * ln) = ln(120)
lnx + (-2ln + lnx) = ln(120)

Reorder the terms:
-2ln + lnx + lnx = ln(120)

Combine like terms: lnx + lnx = 2lnx
-2ln + 2lnx = ln(120)

Reorder the terms for easier multiplication:
-2ln + 2lnx = 120ln

Solving
-2ln + 2lnx = 120ln

Solving for variable 'l'.

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

Add '-120ln' to each side of the equation.
-2ln + -120ln + 2lnx = 120ln + -120ln

Combine like terms: -2ln + -120ln = -122ln
-122ln + 2lnx = 120ln + -120ln

Combine like terms: 120ln + -120ln = 0
-122ln + 2lnx = 0

Factor out the Greatest Common Factor (GCF), '2ln'.
2ln(-61 + 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 '(-61 + x)' equal to zero and attempt to solve: Simplifying -61 + x = 0 Solving -61 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '61' to each side of the equation. -61 + 61 + x = 0 + 61 Combine like terms: -61 + 61 = 0 0 + x = 0 + 61 x = 0 + 61 Combine like terms: 0 + 61 = 61 x = 61 Add '-1x' to each side of the equation. x + -1x = 61 + -1x Combine like terms: x + -1x = 0 0 = 61 + -1x Simplifying 0 = 61 + -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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