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Simplifying ln(12 + -1x) + ln(x + 3) = ln(4x) (12 * ln + -1x * ln) + ln(x + 3) = ln(4x) (12ln + -1lnx) + ln(x + 3) = ln(4x) Reorder the terms: 12ln + -1lnx + ln(3 + x) = ln(4x) 12ln + -1lnx + (3 * ln + x * ln) = ln(4x) 12ln + -1lnx + (3ln + lnx) = ln(4x) Reorder the terms: 12ln + 3ln + -1lnx + lnx = ln(4x) Combine like terms: 12ln + 3ln = 15ln 15ln + -1lnx + lnx = ln(4x) Combine like terms: -1lnx + lnx = 0 15ln + 0 = ln(4x) 15ln = ln(4x) Remove parenthesis around (4x) 15ln = ln * 4x Reorder the terms for easier multiplication: 15ln = 4ln * x Multiply ln * x 15ln = 4lnx Solving 15ln = 4lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-4lnx' to each side of the equation. 15ln + -4lnx = 4lnx + -4lnx Combine like terms: 4lnx + -4lnx = 0 15ln + -4lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(15 + -4x) = 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 '(15 + -4x)' equal to zero and attempt to solve: Simplifying 15 + -4x = 0 Solving 15 + -4x = 0 Move all terms containing l to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + -4x = 0 + -15 Combine like terms: 15 + -15 = 0 0 + -4x = 0 + -15 -4x = 0 + -15 Combine like terms: 0 + -15 = -15 -4x = -15 Add '4x' to each side of the equation. -4x + 4x = -15 + 4x Combine like terms: -4x + 4x = 0 0 = -15 + 4x Simplifying 0 = -15 + 4x 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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