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Simplifying ln(x) + ln(x + 6) = ln(5x + -28) Multiply ln * x lnx + ln(x + 6) = ln(5x + -28) Reorder the terms: lnx + ln(6 + x) = ln(5x + -28) lnx + (6 * ln + x * ln) = ln(5x + -28) lnx + (6ln + lnx) = ln(5x + -28) Reorder the terms: 6ln + lnx + lnx = ln(5x + -28) Combine like terms: lnx + lnx = 2lnx 6ln + 2lnx = ln(5x + -28) Reorder the terms: 6ln + 2lnx = ln(-28 + 5x) 6ln + 2lnx = (-28 * ln + 5x * ln) 6ln + 2lnx = (-28ln + 5lnx) Solving 6ln + 2lnx = -28ln + 5lnx 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. 6ln + 28ln + 2lnx = -28ln + 28ln + 5lnx Combine like terms: 6ln + 28ln = 34ln 34ln + 2lnx = -28ln + 28ln + 5lnx Combine like terms: -28ln + 28ln = 0 34ln + 2lnx = 0 + 5lnx 34ln + 2lnx = 5lnx Add '-5lnx' to each side of the equation. 34ln + 2lnx + -5lnx = 5lnx + -5lnx Combine like terms: 2lnx + -5lnx = -3lnx 34ln + -3lnx = 5lnx + -5lnx Combine like terms: 5lnx + -5lnx = 0 34ln + -3lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(34 + -3x) = 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 '(34 + -3x)' equal to zero and attempt to solve: Simplifying 34 + -3x = 0 Solving 34 + -3x = 0 Move all terms containing l to the left, all other terms to the right. Add '-34' to each side of the equation. 34 + -34 + -3x = 0 + -34 Combine like terms: 34 + -34 = 0 0 + -3x = 0 + -34 -3x = 0 + -34 Combine like terms: 0 + -34 = -34 -3x = -34 Add '3x' to each side of the equation. -3x + 3x = -34 + 3x Combine like terms: -3x + 3x = 0 0 = -34 + 3x Simplifying 0 = -34 + 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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