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Simplifying log(8)(3x + 7) = log(8)(2x + -5) Reorder the terms: glo * 8(7 + 3x) = log(8)(2x + -5) Reorder the terms for easier multiplication: 8glo(7 + 3x) = log(8)(2x + -5) (7 * 8glo + 3x * 8glo) = log(8)(2x + -5) (56glo + 24glox) = log(8)(2x + -5) Reorder the terms: 56glo + 24glox = glo * 8(-5 + 2x) Reorder the terms for easier multiplication: 56glo + 24glox = 8glo(-5 + 2x) 56glo + 24glox = (-5 * 8glo + 2x * 8glo) 56glo + 24glox = (-40glo + 16glox) Solving 56glo + 24glox = -40glo + 16glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '40glo' to each side of the equation. 56glo + 40glo + 24glox = -40glo + 40glo + 16glox Combine like terms: 56glo + 40glo = 96glo 96glo + 24glox = -40glo + 40glo + 16glox Combine like terms: -40glo + 40glo = 0 96glo + 24glox = 0 + 16glox 96glo + 24glox = 16glox Add '-16glox' to each side of the equation. 96glo + 24glox + -16glox = 16glox + -16glox Combine like terms: 24glox + -16glox = 8glox 96glo + 8glox = 16glox + -16glox Combine like terms: 16glox + -16glox = 0 96glo + 8glox = 0 Factor out the Greatest Common Factor (GCF), '8glo'. 8glo(12 + 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 '(12 + x)' equal to zero and attempt to solve: Simplifying 12 + x = 0 Solving 12 + x = 0 Move all terms containing g to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + x = 0 + -12 Combine like terms: 12 + -12 = 0 0 + x = 0 + -12 x = 0 + -12 Combine like terms: 0 + -12 = -12 x = -12 Add '-1x' to each side of the equation. x + -1x = -12 + -1x Combine like terms: x + -1x = 0 0 = -12 + -1x Simplifying 0 = -12 + -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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