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Simplifying ln(5x + 6) = lnx Reorder the terms: ln(6 + 5x) = lnx (6 * ln + 5x * ln) = lnx (6ln + 5lnx) = lnx Solving 6ln + 5lnx = lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-1lnx' to each side of the equation. 6ln + 5lnx + -1lnx = lnx + -1lnx Combine like terms: 5lnx + -1lnx = 4lnx 6ln + 4lnx = lnx + -1lnx Combine like terms: lnx + -1lnx = 0 6ln + 4lnx = 0 Factor out the Greatest Common Factor (GCF), '2ln'. 2ln(3 + 2x) = 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 '(3 + 2x)' equal to zero and attempt to solve: Simplifying 3 + 2x = 0 Solving 3 + 2x = 0 Move all terms containing l to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + 2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2x = 0 + -3 2x = 0 + -3 Combine like terms: 0 + -3 = -3 2x = -3 Add '-2x' to each side of the equation. 2x + -2x = -3 + -2x Combine like terms: 2x + -2x = 0 0 = -3 + -2x Simplifying 0 = -3 + -2x 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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