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Simplifying ln(5x + -3) + -1ln(10x + 7) = 0 Reorder the terms: ln(-3 + 5x) + -1ln(10x + 7) = 0 (-3 * ln + 5x * ln) + -1ln(10x + 7) = 0 (-3ln + 5lnx) + -1ln(10x + 7) = 0 Reorder the terms: -3ln + 5lnx + -1ln(7 + 10x) = 0 -3ln + 5lnx + (7 * -1ln + 10x * -1ln) = 0 -3ln + 5lnx + (-7ln + -10lnx) = 0 Reorder the terms: -3ln + -7ln + 5lnx + -10lnx = 0 Combine like terms: -3ln + -7ln = -10ln -10ln + 5lnx + -10lnx = 0 Combine like terms: 5lnx + -10lnx = -5lnx -10ln + -5lnx = 0 Solving -10ln + -5lnx = 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), '-5ln'. -5ln(2 + x) = 0 Ignore the factor -5.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 '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Add '-1x' to each side of the equation. x + -1x = -2 + -1x Combine like terms: x + -1x = 0 0 = -2 + -1x Simplifying 0 = -2 + -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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