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Simplifying ln(3x + -8) = ln(x + 6) Reorder the terms: ln(-8 + 3x) = ln(x + 6) (-8 * ln + 3x * ln) = ln(x + 6) (-8ln + 3lnx) = ln(x + 6) Reorder the terms: -8ln + 3lnx = ln(6 + x) -8ln + 3lnx = (6 * ln + x * ln) -8ln + 3lnx = (6ln + lnx) Solving -8ln + 3lnx = 6ln + lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-6ln' to each side of the equation. -8ln + -6ln + 3lnx = 6ln + -6ln + lnx Combine like terms: -8ln + -6ln = -14ln -14ln + 3lnx = 6ln + -6ln + lnx Combine like terms: 6ln + -6ln = 0 -14ln + 3lnx = 0 + lnx -14ln + 3lnx = lnx Add '-1lnx' to each side of the equation. -14ln + 3lnx + -1lnx = lnx + -1lnx Combine like terms: 3lnx + -1lnx = 2lnx -14ln + 2lnx = lnx + -1lnx Combine like terms: lnx + -1lnx = 0 -14ln + 2lnx = 0 Factor out the Greatest Common Factor (GCF), '2ln'. 2ln(-7 + 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 '(-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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