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Simplifying ln(x + -6) + ln(5) = ln(30) Reorder the terms: ln(-6 + x) + ln(5) = ln(30) (-6 * ln + x * ln) + ln(5) = ln(30) (-6ln + lnx) + ln(5) = ln(30) Reorder the terms for easier multiplication: -6ln + lnx + 5ln = ln(30) Reorder the terms: -6ln + 5ln + lnx = ln(30) Combine like terms: -6ln + 5ln = -1ln -1ln + lnx = ln(30) Reorder the terms for easier multiplication: -1ln + lnx = 30ln Solving -1ln + lnx = 30ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-30ln' to each side of the equation. -1ln + -30ln + lnx = 30ln + -30ln Combine like terms: -1ln + -30ln = -31ln -31ln + lnx = 30ln + -30ln Combine like terms: 30ln + -30ln = 0 -31ln + lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-31 + x) = 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 '(-31 + x)' equal to zero and attempt to solve: Simplifying -31 + x = 0 Solving -31 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '31' to each side of the equation. -31 + 31 + x = 0 + 31 Combine like terms: -31 + 31 = 0 0 + x = 0 + 31 x = 0 + 31 Combine like terms: 0 + 31 = 31 x = 31 Add '-1x' to each side of the equation. x + -1x = 31 + -1x Combine like terms: x + -1x = 0 0 = 31 + -1x Simplifying 0 = 31 + -1x 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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