ln(y-1)-ln(2)=xln(x)

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


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

Reorder the terms:
ln(-1 + y) + -1ln(2) = xln(x)
(-1 * ln + y * ln) + -1ln(2) = xln(x)
(-1ln + lny) + -1ln(2) = xln(x)

Reorder the terms for easier multiplication:
-1ln + lny + -1 * 2ln = xln(x)

Multiply -1 * 2
-1ln + lny + -2ln = xln(x)

Reorder the terms:
-1ln + -2ln + lny = xln(x)

Combine like terms: -1ln + -2ln = -3ln
-3ln + lny = xln(x)

Multiply lnx * x
-3ln + lny = lnx2

Solving
-3ln + lny = lnx2

Solving for variable 'l'.

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

Add '-1lnx2' to each side of the equation.
-3ln + -1lnx2 + lny = lnx2 + -1lnx2

Combine like terms: lnx2 + -1lnx2 = 0
-3ln + -1lnx2 + lny = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-3 + -1x2 + y) = 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 + -1x2 + y)' equal to zero and attempt to solve: Simplifying -3 + -1x2 + y = 0 Solving -3 + -1x2 + y = 0 Move all terms containing l to the left, all other terms to the right. Add '3' to each side of the equation. -3 + -1x2 + 3 + y = 0 + 3 Reorder the terms: -3 + 3 + -1x2 + y = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1x2 + y = 0 + 3 -1x2 + y = 0 + 3 Combine like terms: 0 + 3 = 3 -1x2 + y = 3 Add 'x2' to each side of the equation. -1x2 + x2 + y = 3 + x2 Combine like terms: -1x2 + x2 = 0 0 + y = 3 + x2 y = 3 + x2 Add '-1y' to each side of the equation. y + -1y = 3 + x2 + -1y Combine like terms: y + -1y = 0 0 = 3 + x2 + -1y Simplifying 0 = 3 + x2 + -1y 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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