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Simplifying ln(3x + 7) = ln(-6x + 19) Reorder the terms: ln(7 + 3x) = ln(-6x + 19) (7 * ln + 3x * ln) = ln(-6x + 19) (7ln + 3lnx) = ln(-6x + 19) Reorder the terms: 7ln + 3lnx = ln(19 + -6x) 7ln + 3lnx = (19 * ln + -6x * ln) 7ln + 3lnx = (19ln + -6lnx) Solving 7ln + 3lnx = 19ln + -6lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-19ln' to each side of the equation. 7ln + -19ln + 3lnx = 19ln + -19ln + -6lnx Combine like terms: 7ln + -19ln = -12ln -12ln + 3lnx = 19ln + -19ln + -6lnx Combine like terms: 19ln + -19ln = 0 -12ln + 3lnx = 0 + -6lnx -12ln + 3lnx = -6lnx Add '6lnx' to each side of the equation. -12ln + 3lnx + 6lnx = -6lnx + 6lnx Combine like terms: 3lnx + 6lnx = 9lnx -12ln + 9lnx = -6lnx + 6lnx Combine like terms: -6lnx + 6lnx = 0 -12ln + 9lnx = 0 Factor out the Greatest Common Factor (GCF), '3ln'. 3ln(-4 + 3x) = 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 + 3x)' equal to zero and attempt to solve: Simplifying -4 + 3x = 0 Solving -4 + 3x = 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 + 3x = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 3x = 0 + 4 3x = 0 + 4 Combine like terms: 0 + 4 = 4 3x = 4 Add '-3x' to each side of the equation. 3x + -3x = 4 + -3x Combine like terms: 3x + -3x = 0 0 = 4 + -3x Simplifying 0 = 4 + -3x 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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