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Simplifying ln(7 + -3x) = ln(2x + 8) (7 * ln + -3x * ln) = ln(2x + 8) (7ln + -3lnx) = ln(2x + 8) Reorder the terms: 7ln + -3lnx = ln(8 + 2x) 7ln + -3lnx = (8 * ln + 2x * ln) 7ln + -3lnx = (8ln + 2lnx) Solving 7ln + -3lnx = 8ln + 2lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-8ln' to each side of the equation. 7ln + -8ln + -3lnx = 8ln + -8ln + 2lnx Combine like terms: 7ln + -8ln = -1ln -1ln + -3lnx = 8ln + -8ln + 2lnx Combine like terms: 8ln + -8ln = 0 -1ln + -3lnx = 0 + 2lnx -1ln + -3lnx = 2lnx Add '-2lnx' to each side of the equation. -1ln + -3lnx + -2lnx = 2lnx + -2lnx Combine like terms: -3lnx + -2lnx = -5lnx -1ln + -5lnx = 2lnx + -2lnx Combine like terms: 2lnx + -2lnx = 0 -1ln + -5lnx = 0 Factor out the Greatest Common Factor (GCF), '-1ln'. -1ln(1 + 5x) = 0 Ignore the factor -1.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 + 5x)' equal to zero and attempt to solve: Simplifying 1 + 5x = 0 Solving 1 + 5x = 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 + 5x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 5x = 0 + -1 5x = 0 + -1 Combine like terms: 0 + -1 = -1 5x = -1 Add '-5x' to each side of the equation. 5x + -5x = -1 + -5x Combine like terms: 5x + -5x = 0 0 = -1 + -5x Simplifying 0 = -1 + -5x 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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