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Simplifying ln(2x + -1) + ln(x + 3) = ln(15) Reorder the terms: ln(-1 + 2x) + ln(x + 3) = ln(15) (-1 * ln + 2x * ln) + ln(x + 3) = ln(15) (-1ln + 2lnx) + ln(x + 3) = ln(15) Reorder the terms: -1ln + 2lnx + ln(3 + x) = ln(15) -1ln + 2lnx + (3 * ln + x * ln) = ln(15) -1ln + 2lnx + (3ln + lnx) = ln(15) Reorder the terms: -1ln + 3ln + 2lnx + lnx = ln(15) Combine like terms: -1ln + 3ln = 2ln 2ln + 2lnx + lnx = ln(15) Combine like terms: 2lnx + lnx = 3lnx 2ln + 3lnx = ln(15) Reorder the terms for easier multiplication: 2ln + 3lnx = 15ln Solving 2ln + 3lnx = 15ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-15ln' to each side of the equation. 2ln + -15ln + 3lnx = 15ln + -15ln Combine like terms: 2ln + -15ln = -13ln -13ln + 3lnx = 15ln + -15ln Combine like terms: 15ln + -15ln = 0 -13ln + 3lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-13 + 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 '(-13 + 3x)' equal to zero and attempt to solve: Simplifying -13 + 3x = 0 Solving -13 + 3x = 0 Move all terms containing l to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + 3x = 0 + 13 Combine like terms: -13 + 13 = 0 0 + 3x = 0 + 13 3x = 0 + 13 Combine like terms: 0 + 13 = 13 3x = 13 Add '-3x' to each side of the equation. 3x + -3x = 13 + -3x Combine like terms: 3x + -3x = 0 0 = 13 + -3x Simplifying 0 = 13 + -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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