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Simplifying 2ln(x + -1) + ln(4) = ln(10 + -3x) Reorder the terms: 2ln(-1 + x) + ln(4) = ln(10 + -3x) (-1 * 2ln + x * 2ln) + ln(4) = ln(10 + -3x) (-2ln + 2lnx) + ln(4) = ln(10 + -3x) Reorder the terms for easier multiplication: -2ln + 2lnx + 4ln = ln(10 + -3x) Reorder the terms: -2ln + 4ln + 2lnx = ln(10 + -3x) Combine like terms: -2ln + 4ln = 2ln 2ln + 2lnx = ln(10 + -3x) 2ln + 2lnx = (10 * ln + -3x * ln) 2ln + 2lnx = (10ln + -3lnx) Solving 2ln + 2lnx = 10ln + -3lnx 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. 2ln + -10ln + 2lnx = 10ln + -10ln + -3lnx Combine like terms: 2ln + -10ln = -8ln -8ln + 2lnx = 10ln + -10ln + -3lnx Combine like terms: 10ln + -10ln = 0 -8ln + 2lnx = 0 + -3lnx -8ln + 2lnx = -3lnx Add '3lnx' to each side of the equation. -8ln + 2lnx + 3lnx = -3lnx + 3lnx Combine like terms: 2lnx + 3lnx = 5lnx -8ln + 5lnx = -3lnx + 3lnx Combine like terms: -3lnx + 3lnx = 0 -8ln + 5lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-8 + 5x) = 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 '(-8 + 5x)' equal to zero and attempt to solve: Simplifying -8 + 5x = 0 Solving -8 + 5x = 0 Move all terms containing l to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + 5x = 0 + 8 Combine like terms: -8 + 8 = 0 0 + 5x = 0 + 8 5x = 0 + 8 Combine like terms: 0 + 8 = 8 5x = 8 Add '-5x' to each side of the equation. 5x + -5x = 8 + -5x Combine like terms: 5x + -5x = 0 0 = 8 + -5x Simplifying 0 = 8 + -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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