ln(15)-ln(x-2)=ln(x)

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Solution for ln(15)-ln(x-2)=ln(x) equation: 


Simplifying
ln(15) + -1ln(x + -2) = ln(x)

Reorder the terms for easier multiplication:
15ln + -1ln(x + -2) = ln(x)

Reorder the terms:
15ln + -1ln(-2 + x) = ln(x)
15ln + (-2 * -1ln + x * -1ln) = ln(x)
15ln + (2ln + -1lnx) = ln(x)

Combine like terms: 15ln + 2ln = 17ln
17ln + -1lnx = ln(x)

Multiply ln * x
17ln + -1lnx = lnx

Solving
17ln + -1lnx = 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.
17ln + -1lnx + -1lnx = lnx + -1lnx

Combine like terms: -1lnx + -1lnx = -2lnx
17ln + -2lnx = lnx + -1lnx

Combine like terms: lnx + -1lnx = 0
17ln + -2lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(17 + -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 '(17 + -2x)' equal to zero and attempt to solve:

Simplifying
17 + -2x = 0

Solving
17 + -2x = 0

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

Add '-17' to each side of the equation.
17 + -17 + -2x = 0 + -17

Combine like terms: 17 + -17 = 0
0 + -2x = 0 + -17
-2x = 0 + -17

Combine like terms: 0 + -17 = -17
-2x = -17

Add '2x' to each side of the equation.
-2x + 2x = -17 + 2x

Combine like terms: -2x + 2x = 0
0 = -17 + 2x

Simplifying
0 = -17 + 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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