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Simplifying ln(x + 31) + -1ln(4 + -3x) = 5ln * 2 Reorder the terms: ln(31 + x) + -1ln(4 + -3x) = 5ln * 2 (31 * ln + x * ln) + -1ln(4 + -3x) = 5ln * 2 (31ln + lnx) + -1ln(4 + -3x) = 5ln * 2 31ln + lnx + (4 * -1ln + -3x * -1ln) = 5ln * 2 31ln + lnx + (-4ln + 3lnx) = 5ln * 2 Reorder the terms: 31ln + -4ln + lnx + 3lnx = 5ln * 2 Combine like terms: 31ln + -4ln = 27ln 27ln + lnx + 3lnx = 5ln * 2 Combine like terms: lnx + 3lnx = 4lnx 27ln + 4lnx = 5ln * 2 Reorder the terms for easier multiplication: 27ln + 4lnx = 5 * 2ln Multiply 5 * 2 27ln + 4lnx = 10ln Solving 27ln + 4lnx = 10ln 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. 27ln + -10ln + 4lnx = 10ln + -10ln Combine like terms: 27ln + -10ln = 17ln 17ln + 4lnx = 10ln + -10ln Combine like terms: 10ln + -10ln = 0 17ln + 4lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(17 + 4x) = 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 '(17 + 4x)' equal to zero and attempt to solve: Simplifying 17 + 4x = 0 Solving 17 + 4x = 0 Move all terms containing l to the left, all other terms to the right. Add '-17' to each side of the equation. 17 + -17 + 4x = 0 + -17 Combine like terms: 17 + -17 = 0 0 + 4x = 0 + -17 4x = 0 + -17 Combine like terms: 0 + -17 = -17 4x = -17 Add '-4x' to each side of the equation. 4x + -4x = -17 + -4x Combine like terms: 4x + -4x = 0 0 = -17 + -4x Simplifying 0 = -17 + -4x 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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