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Simplifying ln(3x + 6) = ln(14x) Reorder the terms: ln(6 + 3x) = ln(14x) (6 * ln + 3x * ln) = ln(14x) (6ln + 3lnx) = ln(14x) Remove parenthesis around (14x) 6ln + 3lnx = ln * 14x Reorder the terms for easier multiplication: 6ln + 3lnx = 14ln * x Multiply ln * x 6ln + 3lnx = 14lnx Solving 6ln + 3lnx = 14lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-14lnx' to each side of the equation. 6ln + 3lnx + -14lnx = 14lnx + -14lnx Combine like terms: 3lnx + -14lnx = -11lnx 6ln + -11lnx = 14lnx + -14lnx Combine like terms: 14lnx + -14lnx = 0 6ln + -11lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(6 + -11x) = 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 + -11x)' equal to zero and attempt to solve: Simplifying 6 + -11x = 0 Solving 6 + -11x = 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 + -11x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -11x = 0 + -6 -11x = 0 + -6 Combine like terms: 0 + -6 = -6 -11x = -6 Add '11x' to each side of the equation. -11x + 11x = -6 + 11x Combine like terms: -11x + 11x = 0 0 = -6 + 11x Simplifying 0 = -6 + 11x 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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