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Simplifying ln(7 + -1x) + ln(3x + 5) = ln(24x) (7 * ln + -1x * ln) + ln(3x + 5) = ln(24x) (7ln + -1lnx) + ln(3x + 5) = ln(24x) Reorder the terms: 7ln + -1lnx + ln(5 + 3x) = ln(24x) 7ln + -1lnx + (5 * ln + 3x * ln) = ln(24x) 7ln + -1lnx + (5ln + 3lnx) = ln(24x) Reorder the terms: 7ln + 5ln + -1lnx + 3lnx = ln(24x) Combine like terms: 7ln + 5ln = 12ln 12ln + -1lnx + 3lnx = ln(24x) Combine like terms: -1lnx + 3lnx = 2lnx 12ln + 2lnx = ln(24x) Remove parenthesis around (24x) 12ln + 2lnx = ln * 24x Reorder the terms for easier multiplication: 12ln + 2lnx = 24ln * x Multiply ln * x 12ln + 2lnx = 24lnx Solving 12ln + 2lnx = 24lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-24lnx' to each side of the equation. 12ln + 2lnx + -24lnx = 24lnx + -24lnx Combine like terms: 2lnx + -24lnx = -22lnx 12ln + -22lnx = 24lnx + -24lnx Combine like terms: 24lnx + -24lnx = 0 12ln + -22lnx = 0 Factor out the Greatest Common Factor (GCF), '2ln'. 2ln(6 + -11x) = 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 '(6 + -11x)' equal to zero and attempt to solve: Simplifying 6 + -11x = 0 Solving 6 + -11x = 0 Move all terms containing l to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -11x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -11x = 0 + -6 -11x = 0 + -6 Combine like terms: 0 + -6 = -6 -11x = -6 Add '11x' to each side of the equation. -11x + 11x = -6 + 11x Combine like terms: -11x + 11x = 0 0 = -6 + 11x Simplifying 0 = -6 + 11x 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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