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Simplifying ln(14) = ln(x + -7) + -1ln(19) Reorder the terms for easier multiplication: 14ln = ln(x + -7) + -1ln(19) Reorder the terms: 14ln = ln(-7 + x) + -1ln(19) 14ln = (-7 * ln + x * ln) + -1ln(19) 14ln = (-7ln + lnx) + -1ln(19) Reorder the terms for easier multiplication: 14ln = -7ln + lnx + -1 * 19ln Multiply -1 * 19 14ln = -7ln + lnx + -19ln Reorder the terms: 14ln = -7ln + -19ln + lnx Combine like terms: -7ln + -19ln = -26ln 14ln = -26ln + lnx Solving 14ln = -26ln + lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '26ln' to each side of the equation. 14ln + 26ln = -26ln + 26ln + lnx Combine like terms: 14ln + 26ln = 40ln 40ln = -26ln + 26ln + lnx Combine like terms: -26ln + 26ln = 0 40ln = 0 + lnx 40ln = lnx Add '-1lnx' to each side of the equation. 40ln + -1lnx = lnx + -1lnx Combine like terms: lnx + -1lnx = 0 40ln + -1lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(40 + -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 '(40 + -1x)' equal to zero and attempt to solve: Simplifying 40 + -1x = 0 Solving 40 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '-40' to each side of the equation. 40 + -40 + -1x = 0 + -40 Combine like terms: 40 + -40 = 0 0 + -1x = 0 + -40 -1x = 0 + -40 Combine like terms: 0 + -40 = -40 -1x = -40 Add 'x' to each side of the equation. -1x + x = -40 + x Combine like terms: -1x + x = 0 0 = -40 + x Simplifying 0 = -40 + 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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