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