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Simplifying ln(15 + 4x) + -2ln(x) = ln(3) (15 * ln + 4x * ln) + -2ln(x) = ln(3) (15ln + 4lnx) + -2ln(x) = ln(3) Multiply ln * x 15ln + 4lnx + -2lnx = ln(3) Combine like terms: 4lnx + -2lnx = 2lnx 15ln + 2lnx = ln(3) Reorder the terms for easier multiplication: 15ln + 2lnx = 3ln Solving 15ln + 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. 15ln + -3ln + 2lnx = 3ln + -3ln Combine like terms: 15ln + -3ln = 12ln 12ln + 2lnx = 3ln + -3ln Combine like terms: 3ln + -3ln = 0 12ln + 2lnx = 0 Factor out the Greatest Common Factor (GCF), '2ln'. 2ln(6 + 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 '(6 + x)' equal to zero and attempt to solve: Simplifying 6 + x = 0 Solving 6 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + x = 0 + -6 x = 0 + -6 Combine like terms: 0 + -6 = -6 x = -6 Add '-1x' to each side of the equation. x + -1x = -6 + -1x Combine like terms: x + -1x = 0 0 = -6 + -1x Simplifying 0 = -6 + -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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