ln(x+10)-ln(x-2)=lnx

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Solution for ln(x+10)-ln(x-2)=lnx equation: 


Simplifying
ln(x + 10) + -1ln(x + -2) = lnx

Reorder the terms:
ln(10 + x) + -1ln(x + -2) = lnx
(10 * ln + x * ln) + -1ln(x + -2) = lnx
(10ln + lnx) + -1ln(x + -2) = lnx

Reorder the terms:
10ln + lnx + -1ln(-2 + x) = lnx
10ln + lnx + (-2 * -1ln + x * -1ln) = lnx
10ln + lnx + (2ln + -1lnx) = lnx

Reorder the terms:
10ln + 2ln + lnx + -1lnx = lnx

Combine like terms: 10ln + 2ln = 12ln
12ln + lnx + -1lnx = lnx

Combine like terms: lnx + -1lnx = 0
12ln + 0 = lnx
12ln = lnx

Solving
12ln = 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.
12ln + -1lnx = lnx + -1lnx

Combine like terms: lnx + -1lnx = 0
12ln + -1lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(12 + -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 '(12 + -1x)' equal to zero and attempt to solve:

Simplifying
12 + -1x = 0

Solving
12 + -1x = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1x = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1x = 0 + -12
-1x = 0 + -12

Combine like terms: 0 + -12 = -12
-1x = -12

Add 'x' to each side of the equation.
-1x + x = -12 + x

Combine like terms: -1x + x = 0
0 = -12 + x

Simplifying
0 = -12 + 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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