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Simplifying ln(4x + -10) + -1ln(2x + 3) = ln(3) Reorder the terms: ln(-10 + 4x) + -1ln(2x + 3) = ln(3) (-10 * ln + 4x * ln) + -1ln(2x + 3) = ln(3) (-10ln + 4lnx) + -1ln(2x + 3) = ln(3) Reorder the terms: -10ln + 4lnx + -1ln(3 + 2x) = ln(3) -10ln + 4lnx + (3 * -1ln + 2x * -1ln) = ln(3) -10ln + 4lnx + (-3ln + -2lnx) = ln(3) Reorder the terms: -10ln + -3ln + 4lnx + -2lnx = ln(3) Combine like terms: -10ln + -3ln = -13ln -13ln + 4lnx + -2lnx = ln(3) Combine like terms: 4lnx + -2lnx = 2lnx -13ln + 2lnx = ln(3) Reorder the terms for easier multiplication: -13ln + 2lnx = 3ln Solving -13ln + 2lnx = 3ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-3ln' to each side of the equation. -13ln + -3ln + 2lnx = 3ln + -3ln Combine like terms: -13ln + -3ln = -16ln -16ln + 2lnx = 3ln + -3ln Combine like terms: 3ln + -3ln = 0 -16ln + 2lnx = 0 Factor out the Greatest Common Factor (GCF), '2ln'. 2ln(-8 + 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 '(-8 + x)' equal to zero and attempt to solve: Simplifying -8 + x = 0 Solving -8 + x = 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 + x = 0 + 8 Combine like terms: -8 + 8 = 0 0 + x = 0 + 8 x = 0 + 8 Combine like terms: 0 + 8 = 8 x = 8 Add '-1x' to each side of the equation. x + -1x = 8 + -1x Combine like terms: x + -1x = 0 0 = 8 + -1x Simplifying 0 = 8 + -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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