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Simplifying ln(6x + 19) = ln(3x + 7) Reorder the terms: ln(19 + 6x) = ln(3x + 7) (19 * ln + 6x * ln) = ln(3x + 7) (19ln + 6lnx) = ln(3x + 7) Reorder the terms: 19ln + 6lnx = ln(7 + 3x) 19ln + 6lnx = (7 * ln + 3x * ln) 19ln + 6lnx = (7ln + 3lnx) Solving 19ln + 6lnx = 7ln + 3lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-7ln' to each side of the equation. 19ln + -7ln + 6lnx = 7ln + -7ln + 3lnx Combine like terms: 19ln + -7ln = 12ln 12ln + 6lnx = 7ln + -7ln + 3lnx Combine like terms: 7ln + -7ln = 0 12ln + 6lnx = 0 + 3lnx 12ln + 6lnx = 3lnx Add '-3lnx' to each side of the equation. 12ln + 6lnx + -3lnx = 3lnx + -3lnx Combine like terms: 6lnx + -3lnx = 3lnx 12ln + 3lnx = 3lnx + -3lnx Combine like terms: 3lnx + -3lnx = 0 12ln + 3lnx = 0 Factor out the Greatest Common Factor (GCF), '3ln'. 3ln(4 + x) = 0 Ignore the factor 3.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 '(4 + x)' equal to zero and attempt to solve: Simplifying 4 + x = 0 Solving 4 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + x = 0 + -4 x = 0 + -4 Combine like terms: 0 + -4 = -4 x = -4 Add '-1x' to each side of the equation. x + -1x = -4 + -1x Combine like terms: x + -1x = 0 0 = -4 + -1x Simplifying 0 = -4 + -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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