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Simplifying log(3x + 7) = log(8x + -13) Reorder the terms: glo(7 + 3x) = log(8x + -13) (7 * glo + 3x * glo) = log(8x + -13) (7glo + 3glox) = log(8x + -13) Reorder the terms: 7glo + 3glox = glo(-13 + 8x) 7glo + 3glox = (-13 * glo + 8x * glo) 7glo + 3glox = (-13glo + 8glox) Solving 7glo + 3glox = -13glo + 8glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '13glo' to each side of the equation. 7glo + 13glo + 3glox = -13glo + 13glo + 8glox Combine like terms: 7glo + 13glo = 20glo 20glo + 3glox = -13glo + 13glo + 8glox Combine like terms: -13glo + 13glo = 0 20glo + 3glox = 0 + 8glox 20glo + 3glox = 8glox Add '-8glox' to each side of the equation. 20glo + 3glox + -8glox = 8glox + -8glox Combine like terms: 3glox + -8glox = -5glox 20glo + -5glox = 8glox + -8glox Combine like terms: 8glox + -8glox = 0 20glo + -5glox = 0 Factor out the Greatest Common Factor (GCF), '5glo'. 5glo(4 + -1x) = 0 Ignore the factor 5.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 '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 0 Move all terms containing g to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Add 'x' to each side of the equation. -1x + x = -4 + x Combine like terms: -1x + x = 0 0 = -4 + x Simplifying 0 = -4 + 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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