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Simplifying ln(x + -2) + ln(x + -1) = ln(4x + -10) Reorder the terms: ln(-2 + x) + ln(x + -1) = ln(4x + -10) (-2 * ln + x * ln) + ln(x + -1) = ln(4x + -10) (-2ln + lnx) + ln(x + -1) = ln(4x + -10) Reorder the terms: -2ln + lnx + ln(-1 + x) = ln(4x + -10) -2ln + lnx + (-1 * ln + x * ln) = ln(4x + -10) -2ln + lnx + (-1ln + lnx) = ln(4x + -10) Reorder the terms: -2ln + -1ln + lnx + lnx = ln(4x + -10) Combine like terms: -2ln + -1ln = -3ln -3ln + lnx + lnx = ln(4x + -10) Combine like terms: lnx + lnx = 2lnx -3ln + 2lnx = ln(4x + -10) Reorder the terms: -3ln + 2lnx = ln(-10 + 4x) -3ln + 2lnx = (-10 * ln + 4x * ln) -3ln + 2lnx = (-10ln + 4lnx) Solving -3ln + 2lnx = -10ln + 4lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '10ln' to each side of the equation. -3ln + 10ln + 2lnx = -10ln + 10ln + 4lnx Combine like terms: -3ln + 10ln = 7ln 7ln + 2lnx = -10ln + 10ln + 4lnx Combine like terms: -10ln + 10ln = 0 7ln + 2lnx = 0 + 4lnx 7ln + 2lnx = 4lnx Add '-4lnx' to each side of the equation. 7ln + 2lnx + -4lnx = 4lnx + -4lnx Combine like terms: 2lnx + -4lnx = -2lnx 7ln + -2lnx = 4lnx + -4lnx Combine like terms: 4lnx + -4lnx = 0 7ln + -2lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(7 + -2x) = 0Subproblem 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 '(7 + -2x)' equal to zero and attempt to solve: Simplifying 7 + -2x = 0 Solving 7 + -2x = 0 Move all terms containing l to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -2x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -2x = 0 + -7 -2x = 0 + -7 Combine like terms: 0 + -7 = -7 -2x = -7 Add '2x' to each side of the equation. -2x + 2x = -7 + 2x Combine like terms: -2x + 2x = 0 0 = -7 + 2x Simplifying 0 = -7 + 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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