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Simplifying ln(3x + -6) = ln(x + 10) Reorder the terms: ln(-6 + 3x) = ln(x + 10) (-6 * ln + 3x * ln) = ln(x + 10) (-6ln + 3lnx) = ln(x + 10) Reorder the terms: -6ln + 3lnx = ln(10 + x) -6ln + 3lnx = (10 * ln + x * ln) -6ln + 3lnx = (10ln + lnx) Solving -6ln + 3lnx = 10ln + lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-10ln' to each side of the equation. -6ln + -10ln + 3lnx = 10ln + -10ln + lnx Combine like terms: -6ln + -10ln = -16ln -16ln + 3lnx = 10ln + -10ln + lnx Combine like terms: 10ln + -10ln = 0 -16ln + 3lnx = 0 + lnx -16ln + 3lnx = lnx Add '-1lnx' to each side of the equation. -16ln + 3lnx + -1lnx = lnx + -1lnx Combine like terms: 3lnx + -1lnx = 2lnx -16ln + 2lnx = lnx + -1lnx Combine like terms: lnx + -1lnx = 0 -16ln + 2lnx = 0 Factor out the Greatest Common Factor (GCF), '2ln'. 2ln(-8 + x) = 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 '(-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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