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Simplifying ln(x + 4) + ln(x + -3) = ln(8x + -22) Reorder the terms: ln(4 + x) + ln(x + -3) = ln(8x + -22) (4 * ln + x * ln) + ln(x + -3) = ln(8x + -22) (4ln + lnx) + ln(x + -3) = ln(8x + -22) Reorder the terms: 4ln + lnx + ln(-3 + x) = ln(8x + -22) 4ln + lnx + (-3 * ln + x * ln) = ln(8x + -22) 4ln + lnx + (-3ln + lnx) = ln(8x + -22) Reorder the terms: 4ln + -3ln + lnx + lnx = ln(8x + -22) Combine like terms: 4ln + -3ln = 1ln 1ln + lnx + lnx = ln(8x + -22) Combine like terms: lnx + lnx = 2lnx 1ln + 2lnx = ln(8x + -22) Reorder the terms: 1ln + 2lnx = ln(-22 + 8x) 1ln + 2lnx = (-22 * ln + 8x * ln) 1ln + 2lnx = (-22ln + 8lnx) Solving 1ln + 2lnx = -22ln + 8lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '22ln' to each side of the equation. 1ln + 22ln + 2lnx = -22ln + 22ln + 8lnx Combine like terms: 1ln + 22ln = 23ln 23ln + 2lnx = -22ln + 22ln + 8lnx Combine like terms: -22ln + 22ln = 0 23ln + 2lnx = 0 + 8lnx 23ln + 2lnx = 8lnx Add '-8lnx' to each side of the equation. 23ln + 2lnx + -8lnx = 8lnx + -8lnx Combine like terms: 2lnx + -8lnx = -6lnx 23ln + -6lnx = 8lnx + -8lnx Combine like terms: 8lnx + -8lnx = 0 23ln + -6lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(23 + -6x) = 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 '(23 + -6x)' equal to zero and attempt to solve: Simplifying 23 + -6x = 0 Solving 23 + -6x = 0 Move all terms containing l to the left, all other terms to the right. Add '-23' to each side of the equation. 23 + -23 + -6x = 0 + -23 Combine like terms: 23 + -23 = 0 0 + -6x = 0 + -23 -6x = 0 + -23 Combine like terms: 0 + -23 = -23 -6x = -23 Add '6x' to each side of the equation. -6x + 6x = -23 + 6x Combine like terms: -6x + 6x = 0 0 = -23 + 6x Simplifying 0 = -23 + 6x 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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