Ln(x^2-9)=ln(x-3)+ln(x+3)

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Solution for Ln(x^2-9)=ln(x-3)+ln(x+3) equation: 


Simplifying
Ln(x2 + -9) = ln(x + -3) + ln(x + 3)

Reorder the terms:
nL(-9 + x2) = ln(x + -3) + ln(x + 3)
(-9 * nL + x2 * nL) = ln(x + -3) + ln(x + 3)
(-9nL + nx2L) = ln(x + -3) + ln(x + 3)

Reorder the terms:
-9nL + nx2L = ln(-3 + x) + ln(x + 3)
-9nL + nx2L = (-3 * ln + x * ln) + ln(x + 3)
-9nL + nx2L = (-3ln + lnx) + ln(x + 3)

Reorder the terms:
-9nL + nx2L = -3ln + lnx + ln(3 + x)
-9nL + nx2L = -3ln + lnx + (3 * ln + x * ln)
-9nL + nx2L = -3ln + lnx + (3ln + lnx)

Reorder the terms:
-9nL + nx2L = -3ln + 3ln + lnx + lnx

Combine like terms: -3ln + 3ln = 0
-9nL + nx2L = 0 + lnx + lnx
-9nL + nx2L = lnx + lnx

Combine like terms: lnx + lnx = 2lnx
-9nL + nx2L = 2lnx

Solving
-9nL + nx2L = 2lnx

Solving for variable 'n'.

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

Add '-2lnx' to each side of the equation.
-9nL + -2lnx + nx2L = 2lnx + -2lnx

Reorder the terms:
-2lnx + -9nL + nx2L = 2lnx + -2lnx

Combine like terms: 2lnx + -2lnx = 0
-2lnx + -9nL + nx2L = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(-2lx + -9L + x2L) = 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 '(-2lx + -9L + x2L)' equal to zero and attempt to solve:

Simplifying
-2lx + -9L + x2L = 0

Reorder the terms:
-9L + -2lx + x2L = 0

Solving
-9L + -2lx + x2L = 0

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

Add '9L' to each side of the equation.
-9L + -2lx + 9L + x2L = 0 + 9L

Reorder the terms:
-9L + 9L + -2lx + x2L = 0 + 9L

Combine like terms: -9L + 9L = 0
0 + -2lx + x2L = 0 + 9L
-2lx + x2L = 0 + 9L
Remove the zero:
-2lx + x2L = 9L

Add '2lx' to each side of the equation.
-2lx + 2lx + x2L = 9L + 2lx

Combine like terms: -2lx + 2lx = 0
0 + x2L = 9L + 2lx
x2L = 9L + 2lx

Add '-1x2L' to each side of the equation.
x2L + -1x2L = 9L + 2lx + -1x2L

Combine like terms: x2L + -1x2L = 0
0 = 9L + 2lx + -1x2L

Simplifying
0 = 9L + 2lx + -1x2L

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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