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Simplifying ln(5x + -6) = ln(18) + -1ln(x + -3) Reorder the terms: ln(-6 + 5x) = ln(18) + -1ln(x + -3) (-6 * ln + 5x * ln) = ln(18) + -1ln(x + -3) (-6ln + 5lnx) = ln(18) + -1ln(x + -3) Reorder the terms for easier multiplication: -6ln + 5lnx = 18ln + -1ln(x + -3) Reorder the terms: -6ln + 5lnx = 18ln + -1ln(-3 + x) -6ln + 5lnx = 18ln + (-3 * -1ln + x * -1ln) -6ln + 5lnx = 18ln + (3ln + -1lnx) Combine like terms: 18ln + 3ln = 21ln -6ln + 5lnx = 21ln + -1lnx Solving -6ln + 5lnx = 21ln + -1lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-21ln' to each side of the equation. -6ln + -21ln + 5lnx = 21ln + -21ln + -1lnx Combine like terms: -6ln + -21ln = -27ln -27ln + 5lnx = 21ln + -21ln + -1lnx Combine like terms: 21ln + -21ln = 0 -27ln + 5lnx = 0 + -1lnx -27ln + 5lnx = -1lnx Add 'lnx' to each side of the equation. -27ln + 5lnx + lnx = -1lnx + lnx Combine like terms: 5lnx + lnx = 6lnx -27ln + 6lnx = -1lnx + lnx Combine like terms: -1lnx + lnx = 0 -27ln + 6lnx = 0 Factor out the Greatest Common Factor (GCF), '3ln'. 3ln(-9 + 2x) = 0 Ignore the factor 3.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 '(-9 + 2x)' equal to zero and attempt to solve: Simplifying -9 + 2x = 0 Solving -9 + 2x = 0 Move all terms containing l to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + 2x = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 2x = 0 + 9 2x = 0 + 9 Combine like terms: 0 + 9 = 9 2x = 9 Add '-2x' to each side of the equation. 2x + -2x = 9 + -2x Combine like terms: 2x + -2x = 0 0 = 9 + -2x Simplifying 0 = 9 + -2x 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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