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Simplifying log(3)(6x + -7) = log(3)(2x + 6) Reorder the terms: glo * 3(-7 + 6x) = log(3)(2x + 6) Reorder the terms for easier multiplication: 3glo(-7 + 6x) = log(3)(2x + 6) (-7 * 3glo + 6x * 3glo) = log(3)(2x + 6) (-21glo + 18glox) = log(3)(2x + 6) Reorder the terms: -21glo + 18glox = glo * 3(6 + 2x) Reorder the terms for easier multiplication: -21glo + 18glox = 3glo(6 + 2x) -21glo + 18glox = (6 * 3glo + 2x * 3glo) -21glo + 18glox = (18glo + 6glox) Solving -21glo + 18glox = 18glo + 6glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-18glo' to each side of the equation. -21glo + -18glo + 18glox = 18glo + -18glo + 6glox Combine like terms: -21glo + -18glo = -39glo -39glo + 18glox = 18glo + -18glo + 6glox Combine like terms: 18glo + -18glo = 0 -39glo + 18glox = 0 + 6glox -39glo + 18glox = 6glox Add '-6glox' to each side of the equation. -39glo + 18glox + -6glox = 6glox + -6glox Combine like terms: 18glox + -6glox = 12glox -39glo + 12glox = 6glox + -6glox Combine like terms: 6glox + -6glox = 0 -39glo + 12glox = 0 Factor out the Greatest Common Factor (GCF), '3glo'. 3glo(-13 + 4x) = 0 Ignore the factor 3.Subproblem 1
Set the factor 'glo' equal to zero and attempt to solve: Simplifying glo = 0 Solving glo = 0 Move all terms containing g to the left, all other terms to the right. Simplifying glo = 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 '(-13 + 4x)' equal to zero and attempt to solve: Simplifying -13 + 4x = 0 Solving -13 + 4x = 0 Move all terms containing g to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + 4x = 0 + 13 Combine like terms: -13 + 13 = 0 0 + 4x = 0 + 13 4x = 0 + 13 Combine like terms: 0 + 13 = 13 4x = 13 Add '-4x' to each side of the equation. 4x + -4x = 13 + -4x Combine like terms: 4x + -4x = 0 0 = 13 + -4x Simplifying 0 = 13 + -4x 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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