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Simplifying 2ln(x + 1) = ln(8x + 28) Reorder the terms: 2ln(1 + x) = ln(8x + 28) (1 * 2ln + x * 2ln) = ln(8x + 28) (2ln + 2lnx) = ln(8x + 28) Reorder the terms: 2ln + 2lnx = ln(28 + 8x) 2ln + 2lnx = (28 * ln + 8x * ln) 2ln + 2lnx = (28ln + 8lnx) Solving 2ln + 2lnx = 28ln + 8lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-28ln' to each side of the equation. 2ln + -28ln + 2lnx = 28ln + -28ln + 8lnx Combine like terms: 2ln + -28ln = -26ln -26ln + 2lnx = 28ln + -28ln + 8lnx Combine like terms: 28ln + -28ln = 0 -26ln + 2lnx = 0 + 8lnx -26ln + 2lnx = 8lnx Add '-8lnx' to each side of the equation. -26ln + 2lnx + -8lnx = 8lnx + -8lnx Combine like terms: 2lnx + -8lnx = -6lnx -26ln + -6lnx = 8lnx + -8lnx Combine like terms: 8lnx + -8lnx = 0 -26ln + -6lnx = 0 Factor out the Greatest Common Factor (GCF), '-2ln'. -2ln(13 + 3x) = 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 '(13 + 3x)' equal to zero and attempt to solve: Simplifying 13 + 3x = 0 Solving 13 + 3x = 0 Move all terms containing l to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + 3x = 0 + -13 Combine like terms: 13 + -13 = 0 0 + 3x = 0 + -13 3x = 0 + -13 Combine like terms: 0 + -13 = -13 3x = -13 Add '-3x' to each side of the equation. 3x + -3x = -13 + -3x Combine like terms: 3x + -3x = 0 0 = -13 + -3x Simplifying 0 = -13 + -3x 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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