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Simplifying log(8)(2x + 7) = log(8)(-4x + -3) Reorder the terms: glo * 8(7 + 2x) = log(8)(-4x + -3) Reorder the terms for easier multiplication: 8glo(7 + 2x) = log(8)(-4x + -3) (7 * 8glo + 2x * 8glo) = log(8)(-4x + -3) (56glo + 16glox) = log(8)(-4x + -3) Reorder the terms: 56glo + 16glox = glo * 8(-3 + -4x) Reorder the terms for easier multiplication: 56glo + 16glox = 8glo(-3 + -4x) 56glo + 16glox = (-3 * 8glo + -4x * 8glo) 56glo + 16glox = (-24glo + -32glox) Solving 56glo + 16glox = -24glo + -32glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '24glo' to each side of the equation. 56glo + 24glo + 16glox = -24glo + 24glo + -32glox Combine like terms: 56glo + 24glo = 80glo 80glo + 16glox = -24glo + 24glo + -32glox Combine like terms: -24glo + 24glo = 0 80glo + 16glox = 0 + -32glox 80glo + 16glox = -32glox Add '32glox' to each side of the equation. 80glo + 16glox + 32glox = -32glox + 32glox Combine like terms: 16glox + 32glox = 48glox 80glo + 48glox = -32glox + 32glox Combine like terms: -32glox + 32glox = 0 80glo + 48glox = 0 Factor out the Greatest Common Factor (GCF), '16glo'. 16glo(5 + 3x) = 0 Ignore the factor 16.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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