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Simplifying ln(5x + 19) = ln(3x + -1) Reorder the terms: ln(19 + 5x) = ln(3x + -1) (19 * ln + 5x * ln) = ln(3x + -1) (19ln + 5lnx) = ln(3x + -1) Reorder the terms: 19ln + 5lnx = ln(-1 + 3x) 19ln + 5lnx = (-1 * ln + 3x * ln) 19ln + 5lnx = (-1ln + 3lnx) Solving 19ln + 5lnx = -1ln + 3lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add 'ln' to each side of the equation. 19ln + ln + 5lnx = -1ln + ln + 3lnx Combine like terms: 19ln + ln = 20ln 20ln + 5lnx = -1ln + ln + 3lnx Combine like terms: -1ln + ln = 0 20ln + 5lnx = 0 + 3lnx 20ln + 5lnx = 3lnx Add '-3lnx' to each side of the equation. 20ln + 5lnx + -3lnx = 3lnx + -3lnx Combine like terms: 5lnx + -3lnx = 2lnx 20ln + 2lnx = 3lnx + -3lnx Combine like terms: 3lnx + -3lnx = 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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