Ln(9+x)=ln(6-x)

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Solution for Ln(9+x)=ln(6-x) equation: 


Simplifying
Ln(9 + x) = ln(6 + -1x)
(9 * nL + x * nL) = ln(6 + -1x)
(9nL + nxL) = ln(6 + -1x)
9nL + nxL = (6 * ln + -1x * ln)
9nL + nxL = (6ln + -1lnx)

Solving
9nL + nxL = 6ln + -1lnx

Solving for variable 'n'.

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

Add '-6ln' to each side of the equation.
9nL + -6ln + nxL = 6ln + -6ln + -1lnx

Reorder the terms:
-6ln + 9nL + nxL = 6ln + -6ln + -1lnx

Combine like terms: 6ln + -6ln = 0
-6ln + 9nL + nxL = 0 + -1lnx
-6ln + 9nL + nxL = -1lnx

Add 'lnx' to each side of the equation.
-6ln + 9nL + lnx + nxL = -1lnx + lnx

Reorder the terms:
-6ln + lnx + 9nL + nxL = -1lnx + lnx

Combine like terms: -1lnx + lnx = 0
-6ln + lnx + 9nL + nxL = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(-6l + lx + 9L + xL) = 0


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

Simplifying
n = 0

Solving
n = 0

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

Simplifying
n = 0

Subproblem 2
Set the factor '(-6l + lx + 9L + xL)' equal to zero and attempt to solve:

Simplifying
-6l + lx + 9L + xL = 0

Reorder the terms:
9L + -6l + lx + xL = 0

Solving
9L + -6l + lx + xL = 0

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

Add '-9L' to each side of the equation.
9L + -6l + lx + -9L + xL = 0 + -9L

Reorder the terms:
9L + -9L + -6l + lx + xL = 0 + -9L

Combine like terms: 9L + -9L = 0
0 + -6l + lx + xL = 0 + -9L
-6l + lx + xL = 0 + -9L
Remove the zero:
-6l + lx + xL = -9L

Add '6l' to each side of the equation.
-6l + lx + 6l + xL = -9L + 6l

Reorder the terms:
-6l + 6l + lx + xL = -9L + 6l

Combine like terms: -6l + 6l = 0
0 + lx + xL = -9L + 6l
lx + xL = -9L + 6l

Add '-1lx' to each side of the equation.
lx + -1lx + xL = -9L + 6l + -1lx

Combine like terms: lx + -1lx = 0
0 + xL = -9L + 6l + -1lx
xL = -9L + 6l + -1lx

Add '-1xL' to each side of the equation.
xL + -1xL = -9L + 6l + -1lx + -1xL

Combine like terms: xL + -1xL = 0
0 = -9L + 6l + -1lx + -1xL

Simplifying
0 = -9L + 6l + -1lx + -1xL

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
n = {0}

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