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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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