ln(x)+ln(x-1)=ln(12)

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Solution for ln(x)+ln(x-1)=ln(12) equation: 


Simplifying
ln(x) + ln(x + -1) = ln(12)

Multiply ln * x
lnx + ln(x + -1) = ln(12)

Reorder the terms:
lnx + ln(-1 + x) = ln(12)
lnx + (-1 * ln + x * ln) = ln(12)
lnx + (-1ln + lnx) = ln(12)

Reorder the terms:
-1ln + lnx + lnx = ln(12)

Combine like terms: lnx + lnx = 2lnx
-1ln + 2lnx = ln(12)

Reorder the terms for easier multiplication:
-1ln + 2lnx = 12ln

Solving
-1ln + 2lnx = 12ln

Solving for variable 'l'.

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

Add '-12ln' to each side of the equation.
-1ln + -12ln + 2lnx = 12ln + -12ln

Combine like terms: -1ln + -12ln = -13ln
-13ln + 2lnx = 12ln + -12ln

Combine like terms: 12ln + -12ln = 0
-13ln + 2lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-13 + 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 '(-13 + 2x)' equal to zero and attempt to solve:

Simplifying
-13 + 2x = 0

Solving
-13 + 2x = 0

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

Add '13' to each side of the equation.
-13 + 13 + 2x = 0 + 13

Combine like terms: -13 + 13 = 0
0 + 2x = 0 + 13
2x = 0 + 13

Combine like terms: 0 + 13 = 13
2x = 13

Add '-2x' to each side of the equation.
2x + -2x = 13 + -2x

Combine like terms: 2x + -2x = 0
0 = 13 + -2x

Simplifying
0 = 13 + -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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