ln(x)+ln(x-1)=ln(2)

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Solution for ln(x)+ln(x-1)=ln(2) equation:


Simplifying
ln(x) + ln(x + -1) = ln(2)

Multiply ln * x
lnx + ln(x + -1) = ln(2)

Reorder the terms:
lnx + ln(-1 + x) = ln(2)
lnx + (-1 * ln + x * ln) = ln(2)
lnx + (-1ln + lnx) = ln(2)

Reorder the terms:
-1ln + lnx + lnx = ln(2)

Combine like terms: lnx + lnx = 2lnx
-1ln + 2lnx = ln(2)

Reorder the terms for easier multiplication:
-1ln + 2lnx = 2ln

Solving
-1ln + 2lnx = 2ln

Solving for variable 'l'.

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

Add '-2ln' to each side of the equation.
-1ln + -2ln + 2lnx = 2ln + -2ln

Combine like terms: -1ln + -2ln = -3ln
-3ln + 2lnx = 2ln + -2ln

Combine like terms: 2ln + -2ln = 0
-3ln + 2lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-3 + 2x) = 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 + 2x)' equal to zero and attempt to solve: Simplifying -3 + 2x = 0 Solving -3 + 2x = 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 + 2x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 2x = 0 + 3 2x = 0 + 3 Combine like terms: 0 + 3 = 3 2x = 3 Add '-2x' to each side of the equation. 2x + -2x = 3 + -2x Combine like terms: 2x + -2x = 0 0 = 3 + -2x Simplifying 0 = 3 + -2x 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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