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Simplifying log(9x + 72) + -1log(2 + -1x) = 2log(x + 6) Reorder the terms: glo(72 + 9x) + -1log(2 + -1x) = 2log(x + 6) (72 * glo + 9x * glo) + -1log(2 + -1x) = 2log(x + 6) (72glo + 9glox) + -1log(2 + -1x) = 2log(x + 6) 72glo + 9glox + (2 * -1glo + -1x * -1glo) = 2log(x + 6) 72glo + 9glox + (-2glo + 1glox) = 2log(x + 6) Reorder the terms: 72glo + -2glo + 9glox + 1glox = 2log(x + 6) Combine like terms: 72glo + -2glo = 70glo 70glo + 9glox + 1glox = 2log(x + 6) Combine like terms: 9glox + 1glox = 10glox 70glo + 10glox = 2log(x + 6) Reorder the terms: 70glo + 10glox = 2glo(6 + x) 70glo + 10glox = (6 * 2glo + x * 2glo) 70glo + 10glox = (12glo + 2glox) Solving 70glo + 10glox = 12glo + 2glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-12glo' to each side of the equation. 70glo + -12glo + 10glox = 12glo + -12glo + 2glox Combine like terms: 70glo + -12glo = 58glo 58glo + 10glox = 12glo + -12glo + 2glox Combine like terms: 12glo + -12glo = 0 58glo + 10glox = 0 + 2glox 58glo + 10glox = 2glox Add '-2glox' to each side of the equation. 58glo + 10glox + -2glox = 2glox + -2glox Combine like terms: 10glox + -2glox = 8glox 58glo + 8glox = 2glox + -2glox Combine like terms: 2glox + -2glox = 0 58glo + 8glox = 0 Factor out the Greatest Common Factor (GCF), '2glo'. 2glo(29 + 4x) = 0 Ignore the factor 2.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 '(29 + 4x)' equal to zero and attempt to solve: Simplifying 29 + 4x = 0 Solving 29 + 4x = 0 Move all terms containing g to the left, all other terms to the right. Add '-29' to each side of the equation. 29 + -29 + 4x = 0 + -29 Combine like terms: 29 + -29 = 0 0 + 4x = 0 + -29 4x = 0 + -29 Combine like terms: 0 + -29 = -29 4x = -29 Add '-4x' to each side of the equation. 4x + -4x = -29 + -4x Combine like terms: 4x + -4x = 0 0 = -29 + -4x Simplifying 0 = -29 + -4x 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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