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Simplifying ln(x) + ln(x + -7) = ln(4x + -24) Multiply ln * x lnx + ln(x + -7) = ln(4x + -24) Reorder the terms: lnx + ln(-7 + x) = ln(4x + -24) lnx + (-7 * ln + x * ln) = ln(4x + -24) lnx + (-7ln + lnx) = ln(4x + -24) Reorder the terms: -7ln + lnx + lnx = ln(4x + -24) Combine like terms: lnx + lnx = 2lnx -7ln + 2lnx = ln(4x + -24) Reorder the terms: -7ln + 2lnx = ln(-24 + 4x) -7ln + 2lnx = (-24 * ln + 4x * ln) -7ln + 2lnx = (-24ln + 4lnx) Solving -7ln + 2lnx = -24ln + 4lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '24ln' to each side of the equation. -7ln + 24ln + 2lnx = -24ln + 24ln + 4lnx Combine like terms: -7ln + 24ln = 17ln 17ln + 2lnx = -24ln + 24ln + 4lnx Combine like terms: -24ln + 24ln = 0 17ln + 2lnx = 0 + 4lnx 17ln + 2lnx = 4lnx Add '-4lnx' to each side of the equation. 17ln + 2lnx + -4lnx = 4lnx + -4lnx Combine like terms: 2lnx + -4lnx = -2lnx 17ln + -2lnx = 4lnx + -4lnx Combine like terms: 4lnx + -4lnx = 0 17ln + -2lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(17 + -2x) = 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 '(17 + -2x)' equal to zero and attempt to solve: Simplifying 17 + -2x = 0 Solving 17 + -2x = 0 Move all terms containing l to the left, all other terms to the right. Add '-17' to each side of the equation. 17 + -17 + -2x = 0 + -17 Combine like terms: 17 + -17 = 0 0 + -2x = 0 + -17 -2x = 0 + -17 Combine like terms: 0 + -17 = -17 -2x = -17 Add '2x' to each side of the equation. -2x + 2x = -17 + 2x Combine like terms: -2x + 2x = 0 0 = -17 + 2x Simplifying 0 = -17 + 2x 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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