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Simplifying ln(3x + -5) + ln(2) + -1ln(6) = 9 Reorder the terms: ln(-5 + 3x) + ln(2) + -1ln(6) = 9 (-5 * ln + 3x * ln) + ln(2) + -1ln(6) = 9 (-5ln + 3lnx) + ln(2) + -1ln(6) = 9 Reorder the terms for easier multiplication: -5ln + 3lnx + 2ln + -1ln(6) = 9 Reorder the terms for easier multiplication: -5ln + 3lnx + 2ln + -1 * 6ln = 9 Multiply -1 * 6 -5ln + 3lnx + 2ln + -6ln = 9 Reorder the terms: -5ln + 2ln + -6ln + 3lnx = 9 Combine like terms: -5ln + 2ln = -3ln -3ln + -6ln + 3lnx = 9 Combine like terms: -3ln + -6ln = -9ln -9ln + 3lnx = 9 Solving -9ln + 3lnx = 9 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Reorder the terms: -9 + -9ln + 3lnx = 9 + -9 Combine like terms: 9 + -9 = 0 -9 + -9ln + 3lnx = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-3 + -3ln + lnx) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-3 + -3ln + lnx)' equal to zero and attempt to solve: Simplifying -3 + -3ln + lnx = 0 Solving -3 + -3ln + lnx = 0 Move all terms containing l to the left, all other terms to the right. Add '3' to each side of the equation. -3 + -3ln + 3 + lnx = 0 + 3 Reorder the terms: -3 + 3 + -3ln + lnx = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -3ln + lnx = 0 + 3 -3ln + lnx = 0 + 3 Combine like terms: 0 + 3 = 3 -3ln + lnx = 3 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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