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Simplifying ln(x) + ln(x + 6) = ln(5x + 12) Multiply ln * x lnx + ln(x + 6) = ln(5x + 12) Reorder the terms: lnx + ln(6 + x) = ln(5x + 12) lnx + (6 * ln + x * ln) = ln(5x + 12) lnx + (6ln + lnx) = ln(5x + 12) Reorder the terms: 6ln + lnx + lnx = ln(5x + 12) Combine like terms: lnx + lnx = 2lnx 6ln + 2lnx = ln(5x + 12) Reorder the terms: 6ln + 2lnx = ln(12 + 5x) 6ln + 2lnx = (12 * ln + 5x * ln) 6ln + 2lnx = (12ln + 5lnx) Solving 6ln + 2lnx = 12ln + 5lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-12ln' to each side of the equation. 6ln + -12ln + 2lnx = 12ln + -12ln + 5lnx Combine like terms: 6ln + -12ln = -6ln -6ln + 2lnx = 12ln + -12ln + 5lnx Combine like terms: 12ln + -12ln = 0 -6ln + 2lnx = 0 + 5lnx -6ln + 2lnx = 5lnx Add '-5lnx' to each side of the equation. -6ln + 2lnx + -5lnx = 5lnx + -5lnx Combine like terms: 2lnx + -5lnx = -3lnx -6ln + -3lnx = 5lnx + -5lnx Combine like terms: 5lnx + -5lnx = 0 -6ln + -3lnx = 0 Factor out the Greatest Common Factor (GCF), '-3ln'. -3ln(2 + x) = 0 Ignore the factor -3.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 '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Add '-1x' to each side of the equation. x + -1x = -2 + -1x Combine like terms: x + -1x = 0 0 = -2 + -1x Simplifying 0 = -2 + -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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