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Simplifying ln(12) = ln(x + 8) + -1ln(19) Reorder the terms for easier multiplication: 12ln = ln(x + 8) + -1ln(19) Reorder the terms: 12ln = ln(8 + x) + -1ln(19) 12ln = (8 * ln + x * ln) + -1ln(19) 12ln = (8ln + lnx) + -1ln(19) Reorder the terms for easier multiplication: 12ln = 8ln + lnx + -1 * 19ln Multiply -1 * 19 12ln = 8ln + lnx + -19ln Reorder the terms: 12ln = 8ln + -19ln + lnx Combine like terms: 8ln + -19ln = -11ln 12ln = -11ln + lnx Solving 12ln = -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. 12ln + 11ln = -11ln + 11ln + lnx Combine like terms: 12ln + 11ln = 23ln 23ln = -11ln + 11ln + lnx Combine like terms: -11ln + 11ln = 0 23ln = 0 + lnx 23ln = lnx Add '-1lnx' to each side of the equation. 23ln + -1lnx = lnx + -1lnx Combine like terms: lnx + -1lnx = 0 23ln + -1lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(23 + -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 '(23 + -1x)' equal to zero and attempt to solve: Simplifying 23 + -1x = 0 Solving 23 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '-23' to each side of the equation. 23 + -23 + -1x = 0 + -23 Combine like terms: 23 + -23 = 0 0 + -1x = 0 + -23 -1x = 0 + -23 Combine like terms: 0 + -23 = -23 -1x = -23 Add 'x' to each side of the equation. -1x + x = -23 + x Combine like terms: -1x + x = 0 0 = -23 + x Simplifying 0 = -23 + 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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