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Simplifying ln(7x + 21) = ln(6x + 15) Reorder the terms: ln(21 + 7x) = ln(6x + 15) (21 * ln + 7x * ln) = ln(6x + 15) (21ln + 7lnx) = ln(6x + 15) Reorder the terms: 21ln + 7lnx = ln(15 + 6x) 21ln + 7lnx = (15 * ln + 6x * ln) 21ln + 7lnx = (15ln + 6lnx) Solving 21ln + 7lnx = 15ln + 6lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-15ln' to each side of the equation. 21ln + -15ln + 7lnx = 15ln + -15ln + 6lnx Combine like terms: 21ln + -15ln = 6ln 6ln + 7lnx = 15ln + -15ln + 6lnx Combine like terms: 15ln + -15ln = 0 6ln + 7lnx = 0 + 6lnx 6ln + 7lnx = 6lnx Add '-6lnx' to each side of the equation. 6ln + 7lnx + -6lnx = 6lnx + -6lnx Combine like terms: 7lnx + -6lnx = 1lnx 6ln + 1lnx = 6lnx + -6lnx Combine like terms: 6lnx + -6lnx = 0 6ln + 1lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(6 + x) = 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 + x)' equal to zero and attempt to solve: Simplifying 6 + x = 0 Solving 6 + x = 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 + x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + x = 0 + -6 x = 0 + -6 Combine like terms: 0 + -6 = -6 x = -6 Add '-1x' to each side of the equation. x + -1x = -6 + -1x Combine like terms: x + -1x = 0 0 = -6 + -1x Simplifying 0 = -6 + -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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