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Simplifying ln(5x + 3) = ln(7) + -1ln(x + -2) Reorder the terms: ln(3 + 5x) = ln(7) + -1ln(x + -2) (3 * ln + 5x * ln) = ln(7) + -1ln(x + -2) (3ln + 5lnx) = ln(7) + -1ln(x + -2) Reorder the terms for easier multiplication: 3ln + 5lnx = 7ln + -1ln(x + -2) Reorder the terms: 3ln + 5lnx = 7ln + -1ln(-2 + x) 3ln + 5lnx = 7ln + (-2 * -1ln + x * -1ln) 3ln + 5lnx = 7ln + (2ln + -1lnx) Combine like terms: 7ln + 2ln = 9ln 3ln + 5lnx = 9ln + -1lnx Solving 3ln + 5lnx = 9ln + -1lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-9ln' to each side of the equation. 3ln + -9ln + 5lnx = 9ln + -9ln + -1lnx Combine like terms: 3ln + -9ln = -6ln -6ln + 5lnx = 9ln + -9ln + -1lnx Combine like terms: 9ln + -9ln = 0 -6ln + 5lnx = 0 + -1lnx -6ln + 5lnx = -1lnx Add 'lnx' to each side of the equation. -6ln + 5lnx + lnx = -1lnx + lnx Combine like terms: 5lnx + lnx = 6lnx -6ln + 6lnx = -1lnx + lnx Combine like terms: -1lnx + lnx = 0 -6ln + 6lnx = 0 Factor out the Greatest Common Factor (GCF), '6ln'. 6ln(-1 + x) = 0 Ignore the factor 6.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 '(-1 + x)' equal to zero and attempt to solve: Simplifying -1 + x = 0 Solving -1 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + x = 0 + 1 x = 0 + 1 Combine like terms: 0 + 1 = 1 x = 1 Add '-1x' to each side of the equation. x + -1x = 1 + -1x Combine like terms: x + -1x = 0 0 = 1 + -1x Simplifying 0 = 1 + -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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