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Simplifying ln(18) = ln(x + -7) + ln(4) Reorder the terms for easier multiplication: 18ln = ln(x + -7) + ln(4) Reorder the terms: 18ln = ln(-7 + x) + ln(4) 18ln = (-7 * ln + x * ln) + ln(4) 18ln = (-7ln + lnx) + ln(4) Reorder the terms for easier multiplication: 18ln = -7ln + lnx + 4ln Reorder the terms: 18ln = -7ln + 4ln + lnx Combine like terms: -7ln + 4ln = -3ln 18ln = -3ln + lnx Solving 18ln = -3ln + lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '3ln' to each side of the equation. 18ln + 3ln = -3ln + 3ln + lnx Combine like terms: 18ln + 3ln = 21ln 21ln = -3ln + 3ln + lnx Combine like terms: -3ln + 3ln = 0 21ln = 0 + lnx 21ln = lnx Add '-1lnx' to each side of the equation. 21ln + -1lnx = lnx + -1lnx Combine like terms: lnx + -1lnx = 0 21ln + -1lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(21 + -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 '(21 + -1x)' equal to zero and attempt to solve: Simplifying 21 + -1x = 0 Solving 21 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '-21' to each side of the equation. 21 + -21 + -1x = 0 + -21 Combine like terms: 21 + -21 = 0 0 + -1x = 0 + -21 -1x = 0 + -21 Combine like terms: 0 + -21 = -21 -1x = -21 Add 'x' to each side of the equation. -1x + x = -21 + x Combine like terms: -1x + x = 0 0 = -21 + x Simplifying 0 = -21 + 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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