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Simplifying log(6)[(2x + 12)(x + 3)] = 2 Reorder the terms: glo * 6[(12 + 2x)(x + 3)] = 2 Reorder the terms: glo * 6[(12 + 2x)(3 + x)] = 2 Multiply (12 + 2x) * (3 + x) glo * 6[(12(3 + x) + 2x * (3 + x))] = 2 glo * 6[((3 * 12 + x * 12) + 2x * (3 + x))] = 2 glo * 6[((36 + 12x) + 2x * (3 + x))] = 2 glo * 6[(36 + 12x + (3 * 2x + x * 2x))] = 2 glo * 6[(36 + 12x + (6x + 2x2))] = 2 Combine like terms: 12x + 6x = 18x glo * 6[(36 + 18x + 2x2)] = 2 Reorder the terms for easier multiplication: 6glo[36 + 18x + 2x2] = 2 [36 * 6glo + 18x * 6glo + 2x2 * 6glo] = 2 [216glo + 108glox + 12glox2] = 2 Solving 216glo + 108glox + 12glox2 = 2 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Reorder the terms: -2 + 216glo + 108glox + 12glox2 = 2 + -2 Combine like terms: 2 + -2 = 0 -2 + 216glo + 108glox + 12glox2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-1 + 108glo + 54glox + 6glox2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + 108glo + 54glox + 6glox2)' equal to zero and attempt to solve: Simplifying -1 + 108glo + 54glox + 6glox2 = 0 Solving -1 + 108glo + 54glox + 6glox2 = 0 Move all terms containing g to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 108glo + 54glox + 1 + 6glox2 = 0 + 1 Reorder the terms: -1 + 1 + 108glo + 54glox + 6glox2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 108glo + 54glox + 6glox2 = 0 + 1 108glo + 54glox + 6glox2 = 0 + 1 Combine like terms: 0 + 1 = 1 108glo + 54glox + 6glox2 = 1 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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