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Simplifying ln(6x + 19) = ln(4x + 1) Reorder the terms: ln(19 + 6x) = ln(4x + 1) (19 * ln + 6x * ln) = ln(4x + 1) (19ln + 6lnx) = ln(4x + 1) Reorder the terms: 19ln + 6lnx = ln(1 + 4x) 19ln + 6lnx = (1 * ln + 4x * ln) 19ln + 6lnx = (1ln + 4lnx) Solving 19ln + 6lnx = 1ln + 4lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-1ln' to each side of the equation. 19ln + -1ln + 6lnx = 1ln + -1ln + 4lnx Combine like terms: 19ln + -1ln = 18ln 18ln + 6lnx = 1ln + -1ln + 4lnx Combine like terms: 1ln + -1ln = 0 18ln + 6lnx = 0 + 4lnx 18ln + 6lnx = 4lnx Add '-4lnx' to each side of the equation. 18ln + 6lnx + -4lnx = 4lnx + -4lnx Combine like terms: 6lnx + -4lnx = 2lnx 18ln + 2lnx = 4lnx + -4lnx Combine like terms: 4lnx + -4lnx = 0 18ln + 2lnx = 0 Factor out the Greatest Common Factor (GCF), '2ln'. 2ln(9 + x) = 0 Ignore the factor 2.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 '(9 + x)' equal to zero and attempt to solve: Simplifying 9 + x = 0 Solving 9 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + x = 0 + -9 x = 0 + -9 Combine like terms: 0 + -9 = -9 x = -9 Add '-1x' to each side of the equation. x + -1x = -9 + -1x Combine like terms: x + -1x = 0 0 = -9 + -1x Simplifying 0 = -9 + -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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