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Simplifying ln(x) + ln(x + -4) = ln(30 + -3x) Multiply ln * x lnx + ln(x + -4) = ln(30 + -3x) Reorder the terms: lnx + ln(-4 + x) = ln(30 + -3x) lnx + (-4 * ln + x * ln) = ln(30 + -3x) lnx + (-4ln + lnx) = ln(30 + -3x) Reorder the terms: -4ln + lnx + lnx = ln(30 + -3x) Combine like terms: lnx + lnx = 2lnx -4ln + 2lnx = ln(30 + -3x) -4ln + 2lnx = (30 * ln + -3x * ln) -4ln + 2lnx = (30ln + -3lnx) Solving -4ln + 2lnx = 30ln + -3lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-30ln' to each side of the equation. -4ln + -30ln + 2lnx = 30ln + -30ln + -3lnx Combine like terms: -4ln + -30ln = -34ln -34ln + 2lnx = 30ln + -30ln + -3lnx Combine like terms: 30ln + -30ln = 0 -34ln + 2lnx = 0 + -3lnx -34ln + 2lnx = -3lnx Add '3lnx' to each side of the equation. -34ln + 2lnx + 3lnx = -3lnx + 3lnx Combine like terms: 2lnx + 3lnx = 5lnx -34ln + 5lnx = -3lnx + 3lnx Combine like terms: -3lnx + 3lnx = 0 -34ln + 5lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-34 + 5x) = 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 + 5x)' equal to zero and attempt to solve: Simplifying -34 + 5x = 0 Solving -34 + 5x = 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 + 5x = 0 + 34 Combine like terms: -34 + 34 = 0 0 + 5x = 0 + 34 5x = 0 + 34 Combine like terms: 0 + 34 = 34 5x = 34 Add '-5x' to each side of the equation. 5x + -5x = 34 + -5x Combine like terms: 5x + -5x = 0 0 = 34 + -5x Simplifying 0 = 34 + -5x 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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