Ln(x-3)+ln(x+3)=ln(2x+24)

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Solution for Ln(x-3)+ln(x+3)=ln(2x+24) equation: 


Simplifying
Ln(x + -3) + ln(x + 3) = ln(2x + 24)

Reorder the terms:
nL(-3 + x) + ln(x + 3) = ln(2x + 24)
(-3 * nL + x * nL) + ln(x + 3) = ln(2x + 24)
(-3nL + nxL) + ln(x + 3) = ln(2x + 24)

Reorder the terms:
-3nL + nxL + ln(3 + x) = ln(2x + 24)
-3nL + nxL + (3 * ln + x * ln) = ln(2x + 24)
-3nL + nxL + (3ln + lnx) = ln(2x + 24)

Reorder the terms:
3ln + lnx + -3nL + nxL = ln(2x + 24)

Reorder the terms:
3ln + lnx + -3nL + nxL = ln(24 + 2x)
3ln + lnx + -3nL + nxL = (24 * ln + 2x * ln)
3ln + lnx + -3nL + nxL = (24ln + 2lnx)

Solving
3ln + lnx + -3nL + nxL = 24ln + 2lnx

Solving for variable 'l'.

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

Add '-24ln' to each side of the equation.
3ln + lnx + -3nL + -24ln + nxL = 24ln + -24ln + 2lnx

Reorder the terms:
3ln + -24ln + lnx + -3nL + nxL = 24ln + -24ln + 2lnx

Combine like terms: 3ln + -24ln = -21ln
-21ln + lnx + -3nL + nxL = 24ln + -24ln + 2lnx

Combine like terms: 24ln + -24ln = 0
-21ln + lnx + -3nL + nxL = 0 + 2lnx
-21ln + lnx + -3nL + nxL = 2lnx

Add '-2lnx' to each side of the equation.
-21ln + lnx + -3nL + -2lnx + nxL = 2lnx + -2lnx

Reorder the terms:
-21ln + lnx + -2lnx + -3nL + nxL = 2lnx + -2lnx

Combine like terms: lnx + -2lnx = -1lnx
-21ln + -1lnx + -3nL + nxL = 2lnx + -2lnx

Combine like terms: 2lnx + -2lnx = 0
-21ln + -1lnx + -3nL + nxL = 0

Add '3nL' to each side of the equation.
-21ln + -1lnx + -3nL + 3nL + nxL = 0 + 3nL

Combine like terms: -3nL + 3nL = 0
-21ln + -1lnx + 0 + nxL = 0 + 3nL
-21ln + -1lnx + nxL = 0 + 3nL
Remove the zero:
-21ln + -1lnx + nxL = 3nL

Add '-1nxL' to each side of the equation.
-21ln + -1lnx + nxL + -1nxL = 3nL + -1nxL

Combine like terms: nxL + -1nxL = 0
-21ln + -1lnx + 0 = 3nL + -1nxL
-21ln + -1lnx = 3nL + -1nxL

Reorder the terms:
-21ln + -1lnx + -3nL + nxL = 3nL + -3nL + -1nxL + nxL

Combine like terms: 3nL + -3nL = 0
-21ln + -1lnx + -3nL + nxL = 0 + -1nxL + nxL
-21ln + -1lnx + -3nL + nxL = -1nxL + nxL

Combine like terms: -1nxL + nxL = 0
-21ln + -1lnx + -3nL + nxL = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(-21l + -1lx + -3L + 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 l to the left, all other terms to the right.

Add '-1n' to each side of the equation.
n + -1n = 0 + -1n
Remove the zero:
0 = -1n

Simplifying
0 = -1n

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 '(-21l + -1lx + -3L + xL)' equal to zero and attempt to solve:

Simplifying
-21l + -1lx + -3L + xL = 0

Reorder the terms:
-3L + -21l + -1lx + xL = 0

Solving
-3L + -21l + -1lx + xL = 0

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

Add '3L' to each side of the equation.
-3L + -21l + -1lx + 3L + xL = 0 + 3L

Reorder the terms:
-3L + 3L + -21l + -1lx + xL = 0 + 3L

Combine like terms: -3L + 3L = 0
0 + -21l + -1lx + xL = 0 + 3L
-21l + -1lx + xL = 0 + 3L
Remove the zero:
-21l + -1lx + xL = 3L

Add '-1xL' to each side of the equation.
-21l + -1lx + xL + -1xL = 3L + -1xL

Combine like terms: xL + -1xL = 0
-21l + -1lx + 0 = 3L + -1xL
-21l + -1lx = 3L + -1xL

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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