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