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Simplifying ln(7x) + -1ln(x + -3) = 0 Remove parenthesis around (7x) ln * 7x + -1ln(x + -3) = 0 Reorder the terms for easier multiplication: 7ln * x + -1ln(x + -3) = 0 Multiply ln * x 7lnx + -1ln(x + -3) = 0 Reorder the terms: 7lnx + -1ln(-3 + x) = 0 7lnx + (-3 * -1ln + x * -1ln) = 0 7lnx + (3ln + -1lnx) = 0 Reorder the terms: 3ln + 7lnx + -1lnx = 0 Combine like terms: 7lnx + -1lnx = 6lnx 3ln + 6lnx = 0 Solving 3ln + 6lnx = 0 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Factor out the Greatest Common Factor (GCF), '3ln'. 3ln(1 + 2x) = 0 Ignore the factor 3.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 '(1 + 2x)' equal to zero and attempt to solve: Simplifying 1 + 2x = 0 Solving 1 + 2x = 0 Move all terms containing l to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2x = 0 + -1 2x = 0 + -1 Combine like terms: 0 + -1 = -1 2x = -1 Add '-2x' to each side of the equation. 2x + -2x = -1 + -2x Combine like terms: 2x + -2x = 0 0 = -1 + -2x Simplifying 0 = -1 + -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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