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Simplifying ln(x) + ln(x + 5) + -1ln(3x + 6) = 0 Multiply ln * x lnx + ln(x + 5) + -1ln(3x + 6) = 0 Reorder the terms: lnx + ln(5 + x) + -1ln(3x + 6) = 0 lnx + (5 * ln + x * ln) + -1ln(3x + 6) = 0 lnx + (5ln + lnx) + -1ln(3x + 6) = 0 Reorder the terms: lnx + 5ln + lnx + -1ln(6 + 3x) = 0 lnx + 5ln + lnx + (6 * -1ln + 3x * -1ln) = 0 lnx + 5ln + lnx + (-6ln + -3lnx) = 0 Reorder the terms: 5ln + -6ln + lnx + lnx + -3lnx = 0 Combine like terms: 5ln + -6ln = -1ln -1ln + lnx + lnx + -3lnx = 0 Combine like terms: lnx + lnx = 2lnx -1ln + 2lnx + -3lnx = 0 Combine like terms: 2lnx + -3lnx = -1lnx -1ln + -1lnx = 0 Solving -1ln + -1lnx = 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), '-1ln'. -1ln(1 + x) = 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 '(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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