ln(9x+72)-ln(2-x)=2ln(x+6)

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Solution for ln(9x+72)-ln(2-x)=2ln(x+6) equation:


Simplifying
ln(9x + 72) + -1ln(2 + -1x) = 2ln(x + 6)

Reorder the terms:
ln(72 + 9x) + -1ln(2 + -1x) = 2ln(x + 6)
(72 * ln + 9x * ln) + -1ln(2 + -1x) = 2ln(x + 6)
(72ln + 9lnx) + -1ln(2 + -1x) = 2ln(x + 6)
72ln + 9lnx + (2 * -1ln + -1x * -1ln) = 2ln(x + 6)
72ln + 9lnx + (-2ln + 1lnx) = 2ln(x + 6)

Reorder the terms:
72ln + -2ln + 9lnx + 1lnx = 2ln(x + 6)

Combine like terms: 72ln + -2ln = 70ln
70ln + 9lnx + 1lnx = 2ln(x + 6)

Combine like terms: 9lnx + 1lnx = 10lnx
70ln + 10lnx = 2ln(x + 6)

Reorder the terms:
70ln + 10lnx = 2ln(6 + x)
70ln + 10lnx = (6 * 2ln + x * 2ln)
70ln + 10lnx = (12ln + 2lnx)

Solving
70ln + 10lnx = 12ln + 2lnx

Solving for variable 'l'.

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

Add '-12ln' to each side of the equation.
70ln + -12ln + 10lnx = 12ln + -12ln + 2lnx

Combine like terms: 70ln + -12ln = 58ln
58ln + 10lnx = 12ln + -12ln + 2lnx

Combine like terms: 12ln + -12ln = 0
58ln + 10lnx = 0 + 2lnx
58ln + 10lnx = 2lnx

Add '-2lnx' to each side of the equation.
58ln + 10lnx + -2lnx = 2lnx + -2lnx

Combine like terms: 10lnx + -2lnx = 8lnx
58ln + 8lnx = 2lnx + -2lnx

Combine like terms: 2lnx + -2lnx = 0
58ln + 8lnx = 0

Factor out the Greatest Common Factor (GCF), '2ln'.
2ln(29 + 4x) = 0

Ignore the factor 2.

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 '(29 + 4x)' equal to zero and attempt to solve: Simplifying 29 + 4x = 0 Solving 29 + 4x = 0 Move all terms containing l to the left, all other terms to the right. Add '-29' to each side of the equation. 29 + -29 + 4x = 0 + -29 Combine like terms: 29 + -29 = 0 0 + 4x = 0 + -29 4x = 0 + -29 Combine like terms: 0 + -29 = -29 4x = -29 Add '-4x' to each side of the equation. 4x + -4x = -29 + -4x Combine like terms: 4x + -4x = 0 0 = -29 + -4x Simplifying 0 = -29 + -4x 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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