ln(9x+24)=ln(4x-16)

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Solution for ln(9x+24)=ln(4x-16) equation:


Simplifying
ln(9x + 24) = ln(4x + -16)

Reorder the terms:
ln(24 + 9x) = ln(4x + -16)
(24 * ln + 9x * ln) = ln(4x + -16)
(24ln + 9lnx) = ln(4x + -16)

Reorder the terms:
24ln + 9lnx = ln(-16 + 4x)
24ln + 9lnx = (-16 * ln + 4x * ln)
24ln + 9lnx = (-16ln + 4lnx)

Solving
24ln + 9lnx = -16ln + 4lnx

Solving for variable 'l'.

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

Add '16ln' to each side of the equation.
24ln + 16ln + 9lnx = -16ln + 16ln + 4lnx

Combine like terms: 24ln + 16ln = 40ln
40ln + 9lnx = -16ln + 16ln + 4lnx

Combine like terms: -16ln + 16ln = 0
40ln + 9lnx = 0 + 4lnx
40ln + 9lnx = 4lnx

Add '-4lnx' to each side of the equation.
40ln + 9lnx + -4lnx = 4lnx + -4lnx

Combine like terms: 9lnx + -4lnx = 5lnx
40ln + 5lnx = 4lnx + -4lnx

Combine like terms: 4lnx + -4lnx = 0
40ln + 5lnx = 0

Factor out the Greatest Common Factor (GCF), '5ln'.
5ln(8 + x) = 0

Ignore the factor 5.

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 '(8 + x)' equal to zero and attempt to solve: Simplifying 8 + x = 0 Solving 8 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + x = 0 + -8 x = 0 + -8 Combine like terms: 0 + -8 = -8 x = -8 Add '-1x' to each side of the equation. x + -1x = -8 + -1x Combine like terms: x + -1x = 0 0 = -8 + -1x Simplifying 0 = -8 + -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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