ln(x)ln(x+4)=ln(15)+ln(3)

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Solution for ln(x)ln(x+4)=ln(15)+ln(3) equation: 


Simplifying
ln(x) * ln(x + 4) = ln(15) + ln(3)

Reorder the terms:
ln * x * ln(4 + x) = ln(15) + ln(3)

Multiply ln * x
lnx * ln(4 + x) = ln(15) + ln(3)

Multiply lnx * ln
l2n2x(4 + x) = ln(15) + ln(3)
(4 * l2n2x + x * l2n2x) = ln(15) + ln(3)
(4l2n2x + l2n2x2) = ln(15) + ln(3)

Reorder the terms for easier multiplication:
4l2n2x + l2n2x2 = 15ln + ln(3)

Reorder the terms for easier multiplication:
4l2n2x + l2n2x2 = 15ln + 3ln

Combine like terms: 15ln + 3ln = 18ln
4l2n2x + l2n2x2 = 18ln

Solving
4l2n2x + l2n2x2 = 18ln

Solving for variable 'l'.

Reorder the terms:
-18ln + 4l2n2x + l2n2x2 = 18ln + -18ln

Combine like terms: 18ln + -18ln = 0
-18ln + 4l2n2x + l2n2x2 = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-18 + 4lnx + 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 '(-18 + 4lnx + lnx2)' equal to zero and attempt to solve:

Simplifying
-18 + 4lnx + lnx2 = 0

Solving
-18 + 4lnx + lnx2 = 0

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

Add '18' to each side of the equation.
-18 + 4lnx + 18 + lnx2 = 0 + 18

Reorder the terms:
-18 + 18 + 4lnx + lnx2 = 0 + 18

Combine like terms: -18 + 18 = 0
0 + 4lnx + lnx2 = 0 + 18
4lnx + lnx2 = 0 + 18

Combine like terms: 0 + 18 = 18
4lnx + lnx2 = 18

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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