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Simplifying ln(2x + -3) = ln(15) + -1ln(x + -5) Reorder the terms: ln(-3 + 2x) = ln(15) + -1ln(x + -5) (-3 * ln + 2x * ln) = ln(15) + -1ln(x + -5) (-3ln + 2lnx) = ln(15) + -1ln(x + -5) Reorder the terms for easier multiplication: -3ln + 2lnx = 15ln + -1ln(x + -5) Reorder the terms: -3ln + 2lnx = 15ln + -1ln(-5 + x) -3ln + 2lnx = 15ln + (-5 * -1ln + x * -1ln) -3ln + 2lnx = 15ln + (5ln + -1lnx) Combine like terms: 15ln + 5ln = 20ln -3ln + 2lnx = 20ln + -1lnx Solving -3ln + 2lnx = 20ln + -1lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-20ln' to each side of the equation. -3ln + -20ln + 2lnx = 20ln + -20ln + -1lnx Combine like terms: -3ln + -20ln = -23ln -23ln + 2lnx = 20ln + -20ln + -1lnx Combine like terms: 20ln + -20ln = 0 -23ln + 2lnx = 0 + -1lnx -23ln + 2lnx = -1lnx Add 'lnx' to each side of the equation. -23ln + 2lnx + lnx = -1lnx + lnx Combine like terms: 2lnx + lnx = 3lnx -23ln + 3lnx = -1lnx + lnx Combine like terms: -1lnx + lnx = 0 -23ln + 3lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-23 + 3x) = 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 '(-23 + 3x)' equal to zero and attempt to solve: Simplifying -23 + 3x = 0 Solving -23 + 3x = 0 Move all terms containing l to the left, all other terms to the right. Add '23' to each side of the equation. -23 + 23 + 3x = 0 + 23 Combine like terms: -23 + 23 = 0 0 + 3x = 0 + 23 3x = 0 + 23 Combine like terms: 0 + 23 = 23 3x = 23 Add '-3x' to each side of the equation. 3x + -3x = 23 + -3x Combine like terms: 3x + -3x = 0 0 = 23 + -3x Simplifying 0 = 23 + -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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