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Simplifying ln(8x + 3) + ln(x + 6) = 0 Reorder the terms: ln(3 + 8x) + ln(x + 6) = 0 (3 * ln + 8x * ln) + ln(x + 6) = 0 (3ln + 8lnx) + ln(x + 6) = 0 Reorder the terms: 3ln + 8lnx + ln(6 + x) = 0 3ln + 8lnx + (6 * ln + x * ln) = 0 3ln + 8lnx + (6ln + lnx) = 0 Reorder the terms: 3ln + 6ln + 8lnx + lnx = 0 Combine like terms: 3ln + 6ln = 9ln 9ln + 8lnx + lnx = 0 Combine like terms: 8lnx + lnx = 9lnx 9ln + 9lnx = 0 Solving 9ln + 9lnx = 0 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Factor out the Greatest Common Factor (GCF), '9ln'. 9ln(1 + x) = 0 Ignore the factor 9.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 '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Add '-1x' to each side of the equation. x + -1x = -1 + -1x Combine like terms: x + -1x = 0 0 = -1 + -1x Simplifying 0 = -1 + -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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