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Simplifying ln(4) = ln(x + 1) + -1ln(12) Reorder the terms for easier multiplication: 4ln = ln(x + 1) + -1ln(12) Reorder the terms: 4ln = ln(1 + x) + -1ln(12) 4ln = (1 * ln + x * ln) + -1ln(12) 4ln = (1ln + lnx) + -1ln(12) Reorder the terms for easier multiplication: 4ln = 1ln + lnx + -1 * 12ln Multiply -1 * 12 4ln = 1ln + lnx + -12ln Reorder the terms: 4ln = 1ln + -12ln + lnx Combine like terms: 1ln + -12ln = -11ln 4ln = -11ln + lnx Solving 4ln = -11ln + lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '11ln' to each side of the equation. 4ln + 11ln = -11ln + 11ln + lnx Combine like terms: 4ln + 11ln = 15ln 15ln = -11ln + 11ln + lnx Combine like terms: -11ln + 11ln = 0 15ln = 0 + lnx 15ln = lnx Add '-1lnx' to each side of the equation. 15ln + -1lnx = lnx + -1lnx Combine like terms: lnx + -1lnx = 0 15ln + -1lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(15 + -1x) = 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 + -1x)' equal to zero and attempt to solve: Simplifying 15 + -1x = 0 Solving 15 + -1x = 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 + -1x = 0 + -15 Combine like terms: 15 + -15 = 0 0 + -1x = 0 + -15 -1x = 0 + -15 Combine like terms: 0 + -15 = -15 -1x = -15 Add 'x' to each side of the equation. -1x + x = -15 + x Combine like terms: -1x + x = 0 0 = -15 + x Simplifying 0 = -15 + x 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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