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