Ln(x+7)-Ln(x-3)=Ln(x)

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Solution for Ln(x+7)-Ln(x-3)=Ln(x) equation: 


Simplifying
Ln(x + 7) + -1Ln(x + -3) = Ln(x)

Reorder the terms:
nL(7 + x) + -1Ln(x + -3) = Ln(x)
(7 * nL + x * nL) + -1Ln(x + -3) = Ln(x)
(7nL + nxL) + -1Ln(x + -3) = Ln(x)

Reorder the terms:
7nL + nxL + -1nL(-3 + x) = Ln(x)
7nL + nxL + (-3 * -1nL + x * -1nL) = Ln(x)
7nL + nxL + (3nL + -1nxL) = Ln(x)

Reorder the terms:
7nL + 3nL + nxL + -1nxL = Ln(x)

Combine like terms: 7nL + 3nL = 10nL
10nL + nxL + -1nxL = Ln(x)

Combine like terms: nxL + -1nxL = 0
10nL + 0 = Ln(x)
10nL = Ln(x)

Multiply nL * x
10nL = nxL

Solving
10nL = nxL

Solving for variable 'n'.

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

Add '-1nxL' to each side of the equation.
10nL + -1nxL = nxL + -1nxL

Combine like terms: nxL + -1nxL = 0
10nL + -1nxL = 0

Factor out the Greatest Common Factor (GCF), 'nL'.
nL(10 + -1x) = 0


Subproblem 1
Set the factor 'nL' equal to zero and attempt to solve:

Simplifying
nL = 0

Solving
nL = 0

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

Simplifying
nL = 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 '(10 + -1x)' equal to zero and attempt to solve:

Simplifying
10 + -1x = 0

Solving
10 + -1x = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1x = 0 + -10
-1x = 0 + -10

Combine like terms: 0 + -10 = -10
-1x = -10

Add 'x' to each side of the equation.
-1x + x = -10 + x

Combine like terms: -1x + x = 0
0 = -10 + x

Simplifying
0 = -10 + 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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