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Simplifying ln(5x + 6) = ln(3x + -8) Reorder the terms: ln(6 + 5x) = ln(3x + -8) (6 * ln + 5x * ln) = ln(3x + -8) (6ln + 5lnx) = ln(3x + -8) Reorder the terms: 6ln + 5lnx = ln(-8 + 3x) 6ln + 5lnx = (-8 * ln + 3x * ln) 6ln + 5lnx = (-8ln + 3lnx) Solving 6ln + 5lnx = -8ln + 3lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '8ln' to each side of the equation. 6ln + 8ln + 5lnx = -8ln + 8ln + 3lnx Combine like terms: 6ln + 8ln = 14ln 14ln + 5lnx = -8ln + 8ln + 3lnx Combine like terms: -8ln + 8ln = 0 14ln + 5lnx = 0 + 3lnx 14ln + 5lnx = 3lnx Add '-3lnx' to each side of the equation. 14ln + 5lnx + -3lnx = 3lnx + -3lnx Combine like terms: 5lnx + -3lnx = 2lnx 14ln + 2lnx = 3lnx + -3lnx Combine like terms: 3lnx + -3lnx = 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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