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Simplifying ln(7x + 27) = ln(5x + 7) Reorder the terms: ln(27 + 7x) = ln(5x + 7) (27 * ln + 7x * ln) = ln(5x + 7) (27ln + 7lnx) = ln(5x + 7) Reorder the terms: 27ln + 7lnx = ln(7 + 5x) 27ln + 7lnx = (7 * ln + 5x * ln) 27ln + 7lnx = (7ln + 5lnx) Solving 27ln + 7lnx = 7ln + 5lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-7ln' to each side of the equation. 27ln + -7ln + 7lnx = 7ln + -7ln + 5lnx Combine like terms: 27ln + -7ln = 20ln 20ln + 7lnx = 7ln + -7ln + 5lnx Combine like terms: 7ln + -7ln = 0 20ln + 7lnx = 0 + 5lnx 20ln + 7lnx = 5lnx Add '-5lnx' to each side of the equation. 20ln + 7lnx + -5lnx = 5lnx + -5lnx Combine like terms: 7lnx + -5lnx = 2lnx 20ln + 2lnx = 5lnx + -5lnx Combine like terms: 5lnx + -5lnx = 0 20ln + 2lnx = 0 Factor out the Greatest Common Factor (GCF), '2ln'. 2ln(10 + 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 '(10 + x)' equal to zero and attempt to solve: Simplifying 10 + x = 0 Solving 10 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = 0 + -10 Combine like terms: 10 + -10 = 0 0 + x = 0 + -10 x = 0 + -10 Combine like terms: 0 + -10 = -10 x = -10 Add '-1x' to each side of the equation. x + -1x = -10 + -1x Combine like terms: x + -1x = 0 0 = -10 + -1x Simplifying 0 = -10 + -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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