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Simplifying ln(3x + -2) + ln(x + 1) = ln(14x + 8) Reorder the terms: ln(-2 + 3x) + ln(x + 1) = ln(14x + 8) (-2 * ln + 3x * ln) + ln(x + 1) = ln(14x + 8) (-2ln + 3lnx) + ln(x + 1) = ln(14x + 8) Reorder the terms: -2ln + 3lnx + ln(1 + x) = ln(14x + 8) -2ln + 3lnx + (1 * ln + x * ln) = ln(14x + 8) -2ln + 3lnx + (1ln + lnx) = ln(14x + 8) Reorder the terms: -2ln + 1ln + 3lnx + lnx = ln(14x + 8) Combine like terms: -2ln + 1ln = -1ln -1ln + 3lnx + lnx = ln(14x + 8) Combine like terms: 3lnx + lnx = 4lnx -1ln + 4lnx = ln(14x + 8) Reorder the terms: -1ln + 4lnx = ln(8 + 14x) -1ln + 4lnx = (8 * ln + 14x * ln) -1ln + 4lnx = (8ln + 14lnx) Solving -1ln + 4lnx = 8ln + 14lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-8ln' to each side of the equation. -1ln + -8ln + 4lnx = 8ln + -8ln + 14lnx Combine like terms: -1ln + -8ln = -9ln -9ln + 4lnx = 8ln + -8ln + 14lnx Combine like terms: 8ln + -8ln = 0 -9ln + 4lnx = 0 + 14lnx -9ln + 4lnx = 14lnx Add '-14lnx' to each side of the equation. -9ln + 4lnx + -14lnx = 14lnx + -14lnx Combine like terms: 4lnx + -14lnx = -10lnx -9ln + -10lnx = 14lnx + -14lnx Combine like terms: 14lnx + -14lnx = 0 -9ln + -10lnx = 0 Factor out the Greatest Common Factor (GCF), '-1ln'. -1ln(9 + 10x) = 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 + 10x)' equal to zero and attempt to solve: Simplifying 9 + 10x = 0 Solving 9 + 10x = 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 + 10x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 10x = 0 + -9 10x = 0 + -9 Combine like terms: 0 + -9 = -9 10x = -9 Add '-10x' to each side of the equation. 10x + -10x = -9 + -10x Combine like terms: 10x + -10x = 0 0 = -9 + -10x Simplifying 0 = -9 + -10x 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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