ln(6x+24)=ln(2x-4)

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Solution for ln(6x+24)=ln(2x-4) equation:


Simplifying
ln(6x + 24) = ln(2x + -4)

Reorder the terms:
ln(24 + 6x) = ln(2x + -4)
(24 * ln + 6x * ln) = ln(2x + -4)
(24ln + 6lnx) = ln(2x + -4)

Reorder the terms:
24ln + 6lnx = ln(-4 + 2x)
24ln + 6lnx = (-4 * ln + 2x * ln)
24ln + 6lnx = (-4ln + 2lnx)

Solving
24ln + 6lnx = -4ln + 2lnx

Solving for variable 'l'.

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

Add '4ln' to each side of the equation.
24ln + 4ln + 6lnx = -4ln + 4ln + 2lnx

Combine like terms: 24ln + 4ln = 28ln
28ln + 6lnx = -4ln + 4ln + 2lnx

Combine like terms: -4ln + 4ln = 0
28ln + 6lnx = 0 + 2lnx
28ln + 6lnx = 2lnx

Add '-2lnx' to each side of the equation.
28ln + 6lnx + -2lnx = 2lnx + -2lnx

Combine like terms: 6lnx + -2lnx = 4lnx
28ln + 4lnx = 2lnx + -2lnx

Combine like terms: 2lnx + -2lnx = 0
28ln + 4lnx = 0

Factor out the Greatest Common Factor (GCF), '4ln'.
4ln(7 + x) = 0

Ignore the factor 4.

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 '(7 + x)' equal to zero and attempt to solve: Simplifying 7 + x = 0 Solving 7 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + x = 0 + -7 x = 0 + -7 Combine like terms: 0 + -7 = -7 x = -7 Add '-1x' to each side of the equation. x + -1x = -7 + -1x Combine like terms: x + -1x = 0 0 = -7 + -1x Simplifying 0 = -7 + -1x 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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