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Simplifying ln(6x + -1) = ln(x + 14) Reorder the terms: ln(-1 + 6x) = ln(x + 14) (-1 * ln + 6x * ln) = ln(x + 14) (-1ln + 6lnx) = ln(x + 14) Reorder the terms: -1ln + 6lnx = ln(14 + x) -1ln + 6lnx = (14 * ln + x * ln) -1ln + 6lnx = (14ln + lnx) Solving -1ln + 6lnx = 14ln + lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-14ln' to each side of the equation. -1ln + -14ln + 6lnx = 14ln + -14ln + lnx Combine like terms: -1ln + -14ln = -15ln -15ln + 6lnx = 14ln + -14ln + lnx Combine like terms: 14ln + -14ln = 0 -15ln + 6lnx = 0 + lnx -15ln + 6lnx = lnx Add '-1lnx' to each side of the equation. -15ln + 6lnx + -1lnx = lnx + -1lnx Combine like terms: 6lnx + -1lnx = 5lnx -15ln + 5lnx = lnx + -1lnx Combine like terms: lnx + -1lnx = 0 -15ln + 5lnx = 0 Factor out the Greatest Common Factor (GCF), '5ln'. 5ln(-3 + x) = 0 Ignore the factor 5.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 + x)' equal to zero and attempt to solve: Simplifying -3 + x = 0 Solving -3 + x = 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 + x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + x = 0 + 3 x = 0 + 3 Combine like terms: 0 + 3 = 3 x = 3 Add '-1x' to each side of the equation. x + -1x = 3 + -1x Combine like terms: x + -1x = 0 0 = 3 + -1x Simplifying 0 = 3 + -1x 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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