ln(x+7)-ln(x-4)=lnx

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Solution for ln(x+7)-ln(x-4)=lnx equation: 


Simplifying
ln(x + 7) + -1ln(x + -4) = lnx

Reorder the terms:
ln(7 + x) + -1ln(x + -4) = lnx
(7 * ln + x * ln) + -1ln(x + -4) = lnx
(7ln + lnx) + -1ln(x + -4) = lnx

Reorder the terms:
7ln + lnx + -1ln(-4 + x) = lnx
7ln + lnx + (-4 * -1ln + x * -1ln) = lnx
7ln + lnx + (4ln + -1lnx) = lnx

Reorder the terms:
7ln + 4ln + lnx + -1lnx = lnx

Combine like terms: 7ln + 4ln = 11ln
11ln + lnx + -1lnx = lnx

Combine like terms: lnx + -1lnx = 0
11ln + 0 = lnx
11ln = lnx

Solving
11ln = 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.
11ln + -1lnx = lnx + -1lnx

Combine like terms: lnx + -1lnx = 0
11ln + -1lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(11 + -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 '(11 + -1x)' equal to zero and attempt to solve:

Simplifying
11 + -1x = 0

Solving
11 + -1x = 0

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

Add '-11' to each side of the equation.
11 + -11 + -1x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -1x = 0 + -11
-1x = 0 + -11

Combine like terms: 0 + -11 = -11
-1x = -11

Add 'x' to each side of the equation.
-1x + x = -11 + x

Combine like terms: -1x + x = 0
0 = -11 + x

Simplifying
0 = -11 + 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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