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Simplifying Log(4n2 + 2n) + -1logn = log(n2 + 5) Reorder the terms: goL(2n + 4n2) + -1logn = log(n2 + 5) (2n * goL + 4n2 * goL) + -1logn = log(n2 + 5) (2gnoL + 4gn2oL) + -1logn = log(n2 + 5) Reorder the terms: -1glno + 2gnoL + 4gn2oL = log(n2 + 5) Reorder the terms: -1glno + 2gnoL + 4gn2oL = glo(5 + n2) -1glno + 2gnoL + 4gn2oL = (5 * glo + n2 * glo) Reorder the terms: -1glno + 2gnoL + 4gn2oL = (gln2o + 5glo) -1glno + 2gnoL + 4gn2oL = (gln2o + 5glo) Solving -1glno + 2gnoL + 4gn2oL = gln2o + 5glo Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-1gln2o' to each side of the equation. -1glno + 2gnoL + -1gln2o + 4gn2oL = gln2o + -1gln2o + 5glo Reorder the terms: -1glno + -1gln2o + 2gnoL + 4gn2oL = gln2o + -1gln2o + 5glo Combine like terms: gln2o + -1gln2o = 0 -1glno + -1gln2o + 2gnoL + 4gn2oL = 0 + 5glo -1glno + -1gln2o + 2gnoL + 4gn2oL = 5glo Add '-5glo' to each side of the equation. -1glno + -1gln2o + 2gnoL + -5glo + 4gn2oL = 5glo + -5glo Reorder the terms: -1glno + -1gln2o + -5glo + 2gnoL + 4gn2oL = 5glo + -5glo Combine like terms: 5glo + -5glo = 0 -1glno + -1gln2o + -5glo + 2gnoL + 4gn2oL = 0 Factor out the Greatest Common Factor (GCF), 'go'. go(-1ln + -1ln2 + -5l + 2nL + 4n2L) = 0Subproblem 1
Set the factor 'go' equal to zero and attempt to solve: Simplifying go = 0 Solving go = 0 Move all terms containing g to the left, all other terms to the right. Simplifying go = 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 '(-1ln + -1ln2 + -5l + 2nL + 4n2L)' equal to zero and attempt to solve: Simplifying -1ln + -1ln2 + -5l + 2nL + 4n2L = 0 Reorder the terms: -5l + -1ln + -1ln2 + 2nL + 4n2L = 0 Solving -5l + -1ln + -1ln2 + 2nL + 4n2L = 0 Move all terms containing g to the left, all other terms to the right. Add '5l' to each side of the equation. -5l + -1ln + -1ln2 + 2nL + 5l + 4n2L = 0 + 5l Reorder the terms: -5l + 5l + -1ln + -1ln2 + 2nL + 4n2L = 0 + 5l Combine like terms: -5l + 5l = 0 0 + -1ln + -1ln2 + 2nL + 4n2L = 0 + 5l -1ln + -1ln2 + 2nL + 4n2L = 0 + 5l Remove the zero: -1ln + -1ln2 + 2nL + 4n2L = 5l Add 'ln' to each side of the equation. -1ln + -1ln2 + 2nL + ln + 4n2L = 5l + ln Reorder the terms: -1ln + ln + -1ln2 + 2nL + 4n2L = 5l + ln Combine like terms: -1ln + ln = 0 0 + -1ln2 + 2nL + 4n2L = 5l + ln -1ln2 + 2nL + 4n2L = 5l + ln Add 'ln2' to each side of the equation. -1ln2 + 2nL + ln2 + 4n2L = 5l + ln + ln2 Reorder the terms: -1ln2 + ln2 + 2nL + 4n2L = 5l + ln + ln2 Combine like terms: -1ln2 + ln2 = 0 0 + 2nL + 4n2L = 5l + ln + ln2 2nL + 4n2L = 5l + ln + ln2 Add '-2nL' to each side of the equation. 2nL + -2nL + 4n2L = 5l + ln + ln2 + -2nL Combine like terms: 2nL + -2nL = 0 0 + 4n2L = 5l + ln + ln2 + -2nL 4n2L = 5l + ln + ln2 + -2nL Add '-4n2L' to each side of the equation. 4n2L + -4n2L = 5l + ln + ln2 + -2nL + -4n2L Combine like terms: 4n2L + -4n2L = 0 0 = 5l + ln + ln2 + -2nL + -4n2L Simplifying 0 = 5l + ln + ln2 + -2nL + -4n2L 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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