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Simplifying log[9](x + 24) + log[9] * x = 2 Reorder the terms: glo * 9(24 + x) + log[9] * x = 2 Reorder the terms for easier multiplication: 9glo(24 + x) + log[9] * x = 2 (24 * 9glo + x * 9glo) + log[9] * x = 2 (216glo + 9glox) + log[9] * x = 2 Reorder the terms for easier multiplication: 216glo + 9glox + 9glo * x = 2 Multiply glo * x 216glo + 9glox + 9glox = 2 Combine like terms: 9glox + 9glox = 18glox 216glo + 18glox = 2 Solving 216glo + 18glox = 2 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Reorder the terms: -2 + 216glo + 18glox = 2 + -2 Combine like terms: 2 + -2 = 0 -2 + 216glo + 18glox = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-1 + 108glo + 9glox) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + 108glo + 9glox)' equal to zero and attempt to solve: Simplifying -1 + 108glo + 9glox = 0 Solving -1 + 108glo + 9glox = 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 + 1 + 9glox = 0 + 1 Reorder the terms: -1 + 1 + 108glo + 9glox = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 108glo + 9glox = 0 + 1 108glo + 9glox = 0 + 1 Combine like terms: 0 + 1 = 1 108glo + 9glox = 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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