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Simplifying ln(2) + ln(x + 11) = ln(4x + -8) Reorder the terms for easier multiplication: 2ln + ln(x + 11) = ln(4x + -8) Reorder the terms: 2ln + ln(11 + x) = ln(4x + -8) 2ln + (11 * ln + x * ln) = ln(4x + -8) 2ln + (11ln + lnx) = ln(4x + -8) Combine like terms: 2ln + 11ln = 13ln 13ln + lnx = ln(4x + -8) Reorder the terms: 13ln + lnx = ln(-8 + 4x) 13ln + lnx = (-8 * ln + 4x * ln) 13ln + lnx = (-8ln + 4lnx) Solving 13ln + lnx = -8ln + 4lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '8ln' to each side of the equation. 13ln + 8ln + lnx = -8ln + 8ln + 4lnx Combine like terms: 13ln + 8ln = 21ln 21ln + lnx = -8ln + 8ln + 4lnx Combine like terms: -8ln + 8ln = 0 21ln + lnx = 0 + 4lnx 21ln + lnx = 4lnx Add '-4lnx' to each side of the equation. 21ln + lnx + -4lnx = 4lnx + -4lnx Combine like terms: lnx + -4lnx = -3lnx 21ln + -3lnx = 4lnx + -4lnx Combine like terms: 4lnx + -4lnx = 0 21ln + -3lnx = 0 Factor out the Greatest Common Factor (GCF), '3ln'. 3ln(7 + -1x) = 0 Ignore the factor 3.Subproblem 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 '(7 + -1x)' equal to zero and attempt to solve: Simplifying 7 + -1x = 0 Solving 7 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1x = 0 + -7 -1x = 0 + -7 Combine like terms: 0 + -7 = -7 -1x = -7 Add 'x' to each side of the equation. -1x + x = -7 + x Combine like terms: -1x + x = 0 0 = -7 + x Simplifying 0 = -7 + 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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