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Simplifying ln(5x + -4) = ln * 8 + -1ln(x + -2) Reorder the terms: ln(-4 + 5x) = ln * 8 + -1ln(x + -2) (-4 * ln + 5x * ln) = ln * 8 + -1ln(x + -2) (-4ln + 5lnx) = ln * 8 + -1ln(x + -2) Reorder the terms for easier multiplication: -4ln + 5lnx = 8ln + -1ln(x + -2) Reorder the terms: -4ln + 5lnx = 8ln + -1ln(-2 + x) -4ln + 5lnx = 8ln + (-2 * -1ln + x * -1ln) -4ln + 5lnx = 8ln + (2ln + -1lnx) Combine like terms: 8ln + 2ln = 10ln -4ln + 5lnx = 10ln + -1lnx Solving -4ln + 5lnx = 10ln + -1lnx 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. -4ln + -10ln + 5lnx = 10ln + -10ln + -1lnx Combine like terms: -4ln + -10ln = -14ln -14ln + 5lnx = 10ln + -10ln + -1lnx Combine like terms: 10ln + -10ln = 0 -14ln + 5lnx = 0 + -1lnx -14ln + 5lnx = -1lnx Add 'lnx' to each side of the equation. -14ln + 5lnx + lnx = -1lnx + lnx Combine like terms: 5lnx + lnx = 6lnx -14ln + 6lnx = -1lnx + lnx Combine like terms: -1lnx + lnx = 0 -14ln + 6lnx = 0 Factor out the Greatest Common Factor (GCF), '2ln'. 2ln(-7 + 3x) = 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 + 3x)' equal to zero and attempt to solve: Simplifying -7 + 3x = 0 Solving -7 + 3x = 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 + 3x = 0 + 7 Combine like terms: -7 + 7 = 0 0 + 3x = 0 + 7 3x = 0 + 7 Combine like terms: 0 + 7 = 7 3x = 7 Add '-3x' to each side of the equation. 3x + -3x = 7 + -3x Combine like terms: 3x + -3x = 0 0 = 7 + -3x Simplifying 0 = 7 + -3x 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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