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Simplifying ln(3x + 5) = ln(12 + -6x) Reorder the terms: ln(5 + 3x) = ln(12 + -6x) (5 * ln + 3x * ln) = ln(12 + -6x) (5ln + 3lnx) = ln(12 + -6x) 5ln + 3lnx = (12 * ln + -6x * ln) 5ln + 3lnx = (12ln + -6lnx) Solving 5ln + 3lnx = 12ln + -6lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-12ln' to each side of the equation. 5ln + -12ln + 3lnx = 12ln + -12ln + -6lnx Combine like terms: 5ln + -12ln = -7ln -7ln + 3lnx = 12ln + -12ln + -6lnx Combine like terms: 12ln + -12ln = 0 -7ln + 3lnx = 0 + -6lnx -7ln + 3lnx = -6lnx Add '6lnx' to each side of the equation. -7ln + 3lnx + 6lnx = -6lnx + 6lnx Combine like terms: 3lnx + 6lnx = 9lnx -7ln + 9lnx = -6lnx + 6lnx Combine like terms: -6lnx + 6lnx = 0 -7ln + 9lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-7 + 9x) = 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 '(-7 + 9x)' equal to zero and attempt to solve: Simplifying -7 + 9x = 0 Solving -7 + 9x = 0 Move all terms containing l to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + 9x = 0 + 7 Combine like terms: -7 + 7 = 0 0 + 9x = 0 + 7 9x = 0 + 7 Combine like terms: 0 + 7 = 7 9x = 7 Add '-9x' to each side of the equation. 9x + -9x = 7 + -9x Combine like terms: 9x + -9x = 0 0 = 7 + -9x Simplifying 0 = 7 + -9x 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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