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

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


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

Multiply ln * y
lny + -1ln(y + -1) = ln(x)

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

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

Combine like terms: lny + -1lny = 0
1ln + 0 = ln(x)
1ln = ln(x)

Multiply ln * x
1ln = lnx

Solving
1ln = lnx

Solving for variable 'l'.

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

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

Combine like terms: lnx + -1lnx = 0
1ln + -1lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(1 + -1x) = 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 '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

Add '-1' to each side of the equation.
1 + -1 + -1x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1x = 0 + -1
-1x = 0 + -1

Combine like terms: 0 + -1 = -1
-1x = -1

Add 'x' to each side of the equation.
-1x + x = -1 + x

Combine like terms: -1x + x = 0
0 = -1 + x

Simplifying
0 = -1 + x

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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