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Simplifying ln(x + 3) + ln(x + -2) = ln(7x + 10) Reorder the terms: ln(3 + x) + ln(x + -2) = ln(7x + 10) (3 * ln + x * ln) + ln(x + -2) = ln(7x + 10) (3ln + lnx) + ln(x + -2) = ln(7x + 10) Reorder the terms: 3ln + lnx + ln(-2 + x) = ln(7x + 10) 3ln + lnx + (-2 * ln + x * ln) = ln(7x + 10) 3ln + lnx + (-2ln + lnx) = ln(7x + 10) Reorder the terms: 3ln + -2ln + lnx + lnx = ln(7x + 10) Combine like terms: 3ln + -2ln = 1ln 1ln + lnx + lnx = ln(7x + 10) Combine like terms: lnx + lnx = 2lnx 1ln + 2lnx = ln(7x + 10) Reorder the terms: 1ln + 2lnx = ln(10 + 7x) 1ln + 2lnx = (10 * ln + 7x * ln) 1ln + 2lnx = (10ln + 7lnx) Solving 1ln + 2lnx = 10ln + 7lnx 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. 1ln + -10ln + 2lnx = 10ln + -10ln + 7lnx Combine like terms: 1ln + -10ln = -9ln -9ln + 2lnx = 10ln + -10ln + 7lnx Combine like terms: 10ln + -10ln = 0 -9ln + 2lnx = 0 + 7lnx -9ln + 2lnx = 7lnx Add '-7lnx' to each side of the equation. -9ln + 2lnx + -7lnx = 7lnx + -7lnx Combine like terms: 2lnx + -7lnx = -5lnx -9ln + -5lnx = 7lnx + -7lnx Combine like terms: 7lnx + -7lnx = 0 -9ln + -5lnx = 0 Factor out the Greatest Common Factor (GCF), '-1ln'. -1ln(9 + 5x) = 0 Ignore the factor -1.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 '(9 + 5x)' equal to zero and attempt to solve: Simplifying 9 + 5x = 0 Solving 9 + 5x = 0 Move all terms containing l to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + 5x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 5x = 0 + -9 5x = 0 + -9 Combine like terms: 0 + -9 = -9 5x = -9 Add '-5x' to each side of the equation. 5x + -5x = -9 + -5x Combine like terms: 5x + -5x = 0 0 = -9 + -5x Simplifying 0 = -9 + -5x 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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