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Simplifying ln(3x + 11) = ln(2x + 1) Reorder the terms: ln(11 + 3x) = ln(2x + 1) (11 * ln + 3x * ln) = ln(2x + 1) (11ln + 3lnx) = ln(2x + 1) Reorder the terms: 11ln + 3lnx = ln(1 + 2x) 11ln + 3lnx = (1 * ln + 2x * ln) 11ln + 3lnx = (1ln + 2lnx) Solving 11ln + 3lnx = 1ln + 2lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-1ln' to each side of the equation. 11ln + -1ln + 3lnx = 1ln + -1ln + 2lnx Combine like terms: 11ln + -1ln = 10ln 10ln + 3lnx = 1ln + -1ln + 2lnx Combine like terms: 1ln + -1ln = 0 10ln + 3lnx = 0 + 2lnx 10ln + 3lnx = 2lnx Add '-2lnx' to each side of the equation. 10ln + 3lnx + -2lnx = 2lnx + -2lnx Combine like terms: 3lnx + -2lnx = 1lnx 10ln + 1lnx = 2lnx + -2lnx Combine like terms: 2lnx + -2lnx = 0 10ln + 1lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(10 + x) = 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 '(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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