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Simplifying log(8x + 3) = log(3x + 13) Reorder the terms: glo(3 + 8x) = log(3x + 13) (3 * glo + 8x * glo) = log(3x + 13) (3glo + 8glox) = log(3x + 13) Reorder the terms: 3glo + 8glox = glo(13 + 3x) 3glo + 8glox = (13 * glo + 3x * glo) 3glo + 8glox = (13glo + 3glox) Solving 3glo + 8glox = 13glo + 3glox 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. 3glo + -13glo + 8glox = 13glo + -13glo + 3glox Combine like terms: 3glo + -13glo = -10glo -10glo + 8glox = 13glo + -13glo + 3glox Combine like terms: 13glo + -13glo = 0 -10glo + 8glox = 0 + 3glox -10glo + 8glox = 3glox Add '-3glox' to each side of the equation. -10glo + 8glox + -3glox = 3glox + -3glox Combine like terms: 8glox + -3glox = 5glox -10glo + 5glox = 3glox + -3glox Combine like terms: 3glox + -3glox = 0 -10glo + 5glox = 0 Factor out the Greatest Common Factor (GCF), '5glo'. 5glo(-2 + x) = 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 '(-2 + x)' equal to zero and attempt to solve: Simplifying -2 + x = 0 Solving -2 + x = 0 Move all terms containing g to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + x = 0 + 2 x = 0 + 2 Combine like terms: 0 + 2 = 2 x = 2 Add '-1x' to each side of the equation. x + -1x = 2 + -1x Combine like terms: x + -1x = 0 0 = 2 + -1x Simplifying 0 = 2 + -1x 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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