8ln(x)-ln(x^6)=ln(4x+12)

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Solution for 8ln(x)-ln(x^6)=ln(4x+12) equation:


Simplifying
8ln(x) + -1ln(x6) = ln(4x + 12)

Multiply ln * x
8lnx + -1ln(x6) = ln(4x + 12)

Multiply ln * x6
8lnx + -1lnx6 = ln(4x + 12)

Reorder the terms:
8lnx + -1lnx6 = ln(12 + 4x)
8lnx + -1lnx6 = (12 * ln + 4x * ln)
8lnx + -1lnx6 = (12ln + 4lnx)

Solving
8lnx + -1lnx6 = 12ln + 4lnx

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.
8lnx + -12ln + -1lnx6 = 12ln + -12ln + 4lnx

Reorder the terms:
-12ln + 8lnx + -1lnx6 = 12ln + -12ln + 4lnx

Combine like terms: 12ln + -12ln = 0
-12ln + 8lnx + -1lnx6 = 0 + 4lnx
-12ln + 8lnx + -1lnx6 = 4lnx

Add '-4lnx' to each side of the equation.
-12ln + 8lnx + -4lnx + -1lnx6 = 4lnx + -4lnx

Combine like terms: 8lnx + -4lnx = 4lnx
-12ln + 4lnx + -1lnx6 = 4lnx + -4lnx

Combine like terms: 4lnx + -4lnx = 0
-12ln + 4lnx + -1lnx6 = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-12 + 4x + -1x6) = 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 '(-12 + 4x + -1x6)' equal to zero and attempt to solve: Simplifying -12 + 4x + -1x6 = 0 Solving -12 + 4x + -1x6 = 0 Move all terms containing l to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 4x + 12 + -1x6 = 0 + 12 Reorder the terms: -12 + 12 + 4x + -1x6 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + 4x + -1x6 = 0 + 12 4x + -1x6 = 0 + 12 Combine like terms: 0 + 12 = 12 4x + -1x6 = 12 Add '-4x' to each side of the equation. 4x + -4x + -1x6 = 12 + -4x Combine like terms: 4x + -4x = 0 0 + -1x6 = 12 + -4x -1x6 = 12 + -4x Add 'x6' to each side of the equation. -1x6 + x6 = 12 + -4x + x6 Combine like terms: -1x6 + x6 = 0 0 = 12 + -4x + x6 Simplifying 0 = 12 + -4x + x6 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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