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Simplifying log(5x + -7) = log(8x + -2) Reorder the terms: glo(-7 + 5x) = log(8x + -2) (-7 * glo + 5x * glo) = log(8x + -2) (-7glo + 5glox) = log(8x + -2) Reorder the terms: -7glo + 5glox = glo(-2 + 8x) -7glo + 5glox = (-2 * glo + 8x * glo) -7glo + 5glox = (-2glo + 8glox) Solving -7glo + 5glox = -2glo + 8glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '2glo' to each side of the equation. -7glo + 2glo + 5glox = -2glo + 2glo + 8glox Combine like terms: -7glo + 2glo = -5glo -5glo + 5glox = -2glo + 2glo + 8glox Combine like terms: -2glo + 2glo = 0 -5glo + 5glox = 0 + 8glox -5glo + 5glox = 8glox Add '-8glox' to each side of the equation. -5glo + 5glox + -8glox = 8glox + -8glox Combine like terms: 5glox + -8glox = -3glox -5glo + -3glox = 8glox + -8glox Combine like terms: 8glox + -8glox = 0 -5glo + -3glox = 0 Factor out the Greatest Common Factor (GCF), '-1glo'. -1glo(5 + 3x) = 0 Ignore the factor -1.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 '(5 + 3x)' equal to zero and attempt to solve: Simplifying 5 + 3x = 0 Solving 5 + 3x = 0 Move all terms containing g to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 3x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 3x = 0 + -5 3x = 0 + -5 Combine like terms: 0 + -5 = -5 3x = -5 Add '-3x' to each side of the equation. 3x + -3x = -5 + -3x Combine like terms: 3x + -3x = 0 0 = -5 + -3x Simplifying 0 = -5 + -3x 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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