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Simplifying ln(x * 2 + 5x + 6) = ln(x + 11) Reorder the terms for easier multiplication: ln(2x + 5x + 6) = ln(x + 11) Reorder the terms: ln(6 + 2x + 5x) = ln(x + 11) Combine like terms: 2x + 5x = 7x ln(6 + 7x) = ln(x + 11) (6 * ln + 7x * ln) = ln(x + 11) (6ln + 7lnx) = ln(x + 11) Reorder the terms: 6ln + 7lnx = ln(11 + x) 6ln + 7lnx = (11 * ln + x * ln) 6ln + 7lnx = (11ln + lnx) Solving 6ln + 7lnx = 11ln + lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-11ln' to each side of the equation. 6ln + -11ln + 7lnx = 11ln + -11ln + lnx Combine like terms: 6ln + -11ln = -5ln -5ln + 7lnx = 11ln + -11ln + lnx Combine like terms: 11ln + -11ln = 0 -5ln + 7lnx = 0 + lnx -5ln + 7lnx = lnx Add '-1lnx' to each side of the equation. -5ln + 7lnx + -1lnx = lnx + -1lnx Combine like terms: 7lnx + -1lnx = 6lnx -5ln + 6lnx = lnx + -1lnx Combine like terms: lnx + -1lnx = 0 -5ln + 6lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-5 + 6x) = 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 '(-5 + 6x)' equal to zero and attempt to solve: Simplifying -5 + 6x = 0 Solving -5 + 6x = 0 Move all terms containing l to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + 6x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 6x = 0 + 5 6x = 0 + 5 Combine like terms: 0 + 5 = 5 6x = 5 Add '-6x' to each side of the equation. 6x + -6x = 5 + -6x Combine like terms: 6x + -6x = 0 0 = 5 + -6x Simplifying 0 = 5 + -6x 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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