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Simplifying ln(-3x + -3) = ln(2x + 10) Reorder the terms: ln(-3 + -3x) = ln(2x + 10) (-3 * ln + -3x * ln) = ln(2x + 10) (-3ln + -3lnx) = ln(2x + 10) Reorder the terms: -3ln + -3lnx = ln(10 + 2x) -3ln + -3lnx = (10 * ln + 2x * ln) -3ln + -3lnx = (10ln + 2lnx) Solving -3ln + -3lnx = 10ln + 2lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-10ln' to each side of the equation. -3ln + -10ln + -3lnx = 10ln + -10ln + 2lnx Combine like terms: -3ln + -10ln = -13ln -13ln + -3lnx = 10ln + -10ln + 2lnx Combine like terms: 10ln + -10ln = 0 -13ln + -3lnx = 0 + 2lnx -13ln + -3lnx = 2lnx Add '-2lnx' to each side of the equation. -13ln + -3lnx + -2lnx = 2lnx + -2lnx Combine like terms: -3lnx + -2lnx = -5lnx -13ln + -5lnx = 2lnx + -2lnx Combine like terms: 2lnx + -2lnx = 0 -13ln + -5lnx = 0 Factor out the Greatest Common Factor (GCF), '-1ln'. -1ln(13 + 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 '(13 + 5x)' equal to zero and attempt to solve: Simplifying 13 + 5x = 0 Solving 13 + 5x = 0 Move all terms containing l to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + 5x = 0 + -13 Combine like terms: 13 + -13 = 0 0 + 5x = 0 + -13 5x = 0 + -13 Combine like terms: 0 + -13 = -13 5x = -13 Add '-5x' to each side of the equation. 5x + -5x = -13 + -5x Combine like terms: 5x + -5x = 0 0 = -13 + -5x Simplifying 0 = -13 + -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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