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Simplifying ln(2x + 1) + ln(x + -3) = ln(x + 5) Reorder the terms: ln(1 + 2x) + ln(x + -3) = ln(x + 5) (1 * ln + 2x * ln) + ln(x + -3) = ln(x + 5) (1ln + 2lnx) + ln(x + -3) = ln(x + 5) Reorder the terms: 1ln + 2lnx + ln(-3 + x) = ln(x + 5) 1ln + 2lnx + (-3 * ln + x * ln) = ln(x + 5) 1ln + 2lnx + (-3ln + lnx) = ln(x + 5) Reorder the terms: 1ln + -3ln + 2lnx + lnx = ln(x + 5) Combine like terms: 1ln + -3ln = -2ln -2ln + 2lnx + lnx = ln(x + 5) Combine like terms: 2lnx + lnx = 3lnx -2ln + 3lnx = ln(x + 5) Reorder the terms: -2ln + 3lnx = ln(5 + x) -2ln + 3lnx = (5 * ln + x * ln) -2ln + 3lnx = (5ln + lnx) Solving -2ln + 3lnx = 5ln + lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-5ln' to each side of the equation. -2ln + -5ln + 3lnx = 5ln + -5ln + lnx Combine like terms: -2ln + -5ln = -7ln -7ln + 3lnx = 5ln + -5ln + lnx Combine like terms: 5ln + -5ln = 0 -7ln + 3lnx = 0 + lnx -7ln + 3lnx = lnx Add '-1lnx' to each side of the equation. -7ln + 3lnx + -1lnx = lnx + -1lnx Combine like terms: 3lnx + -1lnx = 2lnx -7ln + 2lnx = lnx + -1lnx Combine like terms: lnx + -1lnx = 0 -7ln + 2lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-7 + 2x) = 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 '(-7 + 2x)' equal to zero and attempt to solve: Simplifying -7 + 2x = 0 Solving -7 + 2x = 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 + 2x = 0 + 7 Combine like terms: -7 + 7 = 0 0 + 2x = 0 + 7 2x = 0 + 7 Combine like terms: 0 + 7 = 7 2x = 7 Add '-2x' to each side of the equation. 2x + -2x = 7 + -2x Combine like terms: 2x + -2x = 0 0 = 7 + -2x Simplifying 0 = 7 + -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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