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Simplifying ln(3x + -3) = ln(5x + 7) Reorder the terms: ln(-3 + 3x) = ln(5x + 7) (-3 * ln + 3x * ln) = ln(5x + 7) (-3ln + 3lnx) = ln(5x + 7) Reorder the terms: -3ln + 3lnx = ln(7 + 5x) -3ln + 3lnx = (7 * ln + 5x * ln) -3ln + 3lnx = (7ln + 5lnx) Solving -3ln + 3lnx = 7ln + 5lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-7ln' to each side of the equation. -3ln + -7ln + 3lnx = 7ln + -7ln + 5lnx Combine like terms: -3ln + -7ln = -10ln -10ln + 3lnx = 7ln + -7ln + 5lnx Combine like terms: 7ln + -7ln = 0 -10ln + 3lnx = 0 + 5lnx -10ln + 3lnx = 5lnx Add '-5lnx' to each side of the equation. -10ln + 3lnx + -5lnx = 5lnx + -5lnx Combine like terms: 3lnx + -5lnx = -2lnx -10ln + -2lnx = 5lnx + -5lnx Combine like terms: 5lnx + -5lnx = 0 -10ln + -2lnx = 0 Factor out the Greatest Common Factor (GCF), '-2ln'. -2ln(5 + x) = 0 Ignore the factor -2.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 '(5 + x)' equal to zero and attempt to solve: Simplifying 5 + x = 0 Solving 5 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + x = 0 + -5 x = 0 + -5 Combine like terms: 0 + -5 = -5 x = -5 Add '-1x' to each side of the equation. x + -1x = -5 + -1x Combine like terms: x + -1x = 0 0 = -5 + -1x Simplifying 0 = -5 + -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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