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Simplifying ln(5z + 6) = ln(3x + -8) Reorder the terms: ln(6 + 5z) = ln(3x + -8) (6 * ln + 5z * ln) = ln(3x + -8) (6ln + 5lnz) = ln(3x + -8) Reorder the terms: 6ln + 5lnz = ln(-8 + 3x) 6ln + 5lnz = (-8 * ln + 3x * ln) 6ln + 5lnz = (-8ln + 3lnx) Solving 6ln + 5lnz = -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 + 5lnz = -8ln + 8ln + 3lnx Combine like terms: 6ln + 8ln = 14ln 14ln + 5lnz = -8ln + 8ln + 3lnx Combine like terms: -8ln + 8ln = 0 14ln + 5lnz = 0 + 3lnx 14ln + 5lnz = 3lnx Add '-3lnx' to each side of the equation. 14ln + -3lnx + 5lnz = 3lnx + -3lnx Combine like terms: 3lnx + -3lnx = 0 14ln + -3lnx + 5lnz = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(14 + -3x + 5z) = 0Subproblem 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 '(14 + -3x + 5z)' equal to zero and attempt to solve: Simplifying 14 + -3x + 5z = 0 Solving 14 + -3x + 5z = 0 Move all terms containing l to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -3x + -14 + 5z = 0 + -14 Reorder the terms: 14 + -14 + -3x + 5z = 0 + -14 Combine like terms: 14 + -14 = 0 0 + -3x + 5z = 0 + -14 -3x + 5z = 0 + -14 Combine like terms: 0 + -14 = -14 -3x + 5z = -14 Add '3x' to each side of the equation. -3x + 3x + 5z = -14 + 3x Combine like terms: -3x + 3x = 0 0 + 5z = -14 + 3x 5z = -14 + 3x Add '-5z' to each side of the equation. 5z + -5z = -14 + 3x + -5z Combine like terms: 5z + -5z = 0 0 = -14 + 3x + -5z Simplifying 0 = -14 + 3x + -5z 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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