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Simplifying ln(x + -4) = ln(6x) Reorder the terms: ln(-4 + x) = ln(6x) (-4 * ln + x * ln) = ln(6x) (-4ln + lnx) = ln(6x) Remove parenthesis around (6x) -4ln + lnx = ln * 6x Reorder the terms for easier multiplication: -4ln + lnx = 6ln * x Multiply ln * x -4ln + lnx = 6lnx Solving -4ln + lnx = 6lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-6lnx' to each side of the equation. -4ln + lnx + -6lnx = 6lnx + -6lnx Combine like terms: lnx + -6lnx = -5lnx -4ln + -5lnx = 6lnx + -6lnx Combine like terms: 6lnx + -6lnx = 0 -4ln + -5lnx = 0 Factor out the Greatest Common Factor (GCF), '-1ln'. -1ln(4 + 5x) = 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 '(4 + 5x)' equal to zero and attempt to solve: Simplifying 4 + 5x = 0 Solving 4 + 5x = 0 Move all terms containing l to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + 5x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 5x = 0 + -4 5x = 0 + -4 Combine like terms: 0 + -4 = -4 5x = -4 Add '-5x' to each side of the equation. 5x + -5x = -4 + -5x Combine like terms: 5x + -5x = 0 0 = -4 + -5x Simplifying 0 = -4 + -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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