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Simplifying log(8)(2 + -5x) = log(8)(-4x + 3) Reorder the terms for easier multiplication: 8glo(2 + -5x) = log(8)(-4x + 3) (2 * 8glo + -5x * 8glo) = log(8)(-4x + 3) (16glo + -40glox) = log(8)(-4x + 3) Reorder the terms: 16glo + -40glox = glo * 8(3 + -4x) Reorder the terms for easier multiplication: 16glo + -40glox = 8glo(3 + -4x) 16glo + -40glox = (3 * 8glo + -4x * 8glo) 16glo + -40glox = (24glo + -32glox) Solving 16glo + -40glox = 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. 16glo + -24glo + -40glox = 24glo + -24glo + -32glox Combine like terms: 16glo + -24glo = -8glo -8glo + -40glox = 24glo + -24glo + -32glox Combine like terms: 24glo + -24glo = 0 -8glo + -40glox = 0 + -32glox -8glo + -40glox = -32glox Add '32glox' to each side of the equation. -8glo + -40glox + 32glox = -32glox + 32glox Combine like terms: -40glox + 32glox = -8glox -8glo + -8glox = -32glox + 32glox Combine like terms: -32glox + 32glox = 0 -8glo + -8glox = 0 Factor out the Greatest Common Factor (GCF), '-8glo'. -8glo(1 + x) = 0 Ignore the factor -8.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 '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 0 Move all terms containing g to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Add '-1x' to each side of the equation. x + -1x = -1 + -1x Combine like terms: x + -1x = 0 0 = -1 + -1x Simplifying 0 = -1 + -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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