ln(x+2)ln(x+4)=ln(48)

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Solution for ln(x+2)ln(x+4)=ln(48) equation: 


Simplifying
ln(x + 2) * ln(x + 4) = ln(48)

Reorder the terms:
ln(2 + x) * ln(x + 4) = ln(48)

Reorder the terms:
ln(2 + x) * ln(4 + x) = ln(48)

Reorder the terms for easier multiplication:
ln * ln(2 + x)(4 + x) = ln(48)

Multiply ln * ln
l2n2(2 + x)(4 + x) = ln(48)

Multiply (2 + x) * (4 + x)
l2n2(2(4 + x) + x(4 + x)) = ln(48)
l2n2((4 * 2 + x * 2) + x(4 + x)) = ln(48)
l2n2((8 + 2x) + x(4 + x)) = ln(48)
l2n2(8 + 2x + (4 * x + x * x)) = ln(48)
l2n2(8 + 2x + (4x + x2)) = ln(48)

Combine like terms: 2x + 4x = 6x
l2n2(8 + 6x + x2) = ln(48)
(8 * l2n2 + 6x * l2n2 + x2 * l2n2) = ln(48)
(8l2n2 + 6l2n2x + l2n2x2) = ln(48)

Reorder the terms for easier multiplication:
8l2n2 + 6l2n2x + l2n2x2 = 48ln

Solving
8l2n2 + 6l2n2x + l2n2x2 = 48ln

Solving for variable 'l'.

Reorder the terms:
-48ln + 8l2n2 + 6l2n2x + l2n2x2 = 48ln + -48ln

Combine like terms: 48ln + -48ln = 0
-48ln + 8l2n2 + 6l2n2x + l2n2x2 = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-48 + 8ln + 6lnx + lnx2) = 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 '(-48 + 8ln + 6lnx + lnx2)' equal to zero and attempt to solve:

Simplifying
-48 + 8ln + 6lnx + lnx2 = 0

Solving
-48 + 8ln + 6lnx + lnx2 = 0

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

Add '48' to each side of the equation.
-48 + 8ln + 6lnx + 48 + lnx2 = 0 + 48

Reorder the terms:
-48 + 48 + 8ln + 6lnx + lnx2 = 0 + 48

Combine like terms: -48 + 48 = 0
0 + 8ln + 6lnx + lnx2 = 0 + 48
8ln + 6lnx + lnx2 = 0 + 48

Combine like terms: 0 + 48 = 48
8ln + 6lnx + lnx2 = 48

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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