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Simplifying log[3](1 + -1x) = 1 + log[3](x + 11) Reorder the terms for easier multiplication: 3glo(1 + -1x) = 1 + log[3](x + 11) (1 * 3glo + -1x * 3glo) = 1 + log[3](x + 11) (3glo + -3glox) = 1 + log[3](x + 11) Reorder the terms: 3glo + -3glox = 1 + glo * 3(11 + x) Reorder the terms for easier multiplication: 3glo + -3glox = 1 + 3glo(11 + x) 3glo + -3glox = 1 + (11 * 3glo + x * 3glo) 3glo + -3glox = 1 + (33glo + 3glox) Solving 3glo + -3glox = 1 + 33glo + 3glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-33glo' to each side of the equation. 3glo + -33glo + -3glox = 1 + 33glo + -33glo + 3glox Combine like terms: 3glo + -33glo = -30glo -30glo + -3glox = 1 + 33glo + -33glo + 3glox Combine like terms: 33glo + -33glo = 0 -30glo + -3glox = 1 + 0 + 3glox -30glo + -3glox = 1 + 3glox Add '-3glox' to each side of the equation. -30glo + -3glox + -3glox = 1 + 3glox + -3glox Combine like terms: -3glox + -3glox = -6glox -30glo + -6glox = 1 + 3glox + -3glox Combine like terms: 3glox + -3glox = 0 -30glo + -6glox = 1 + 0 -30glo + -6glox = 1 Reorder the terms: -1 + -30glo + -6glox = 1 + -1 Combine like terms: 1 + -1 = 0 -1 + -30glo + -6glox = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(1 + 30glo + 6glox) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(1 + 30glo + 6glox)' equal to zero and attempt to solve: Simplifying 1 + 30glo + 6glox = 0 Solving 1 + 30glo + 6glox = 0 Move all terms containing g to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + 30glo + -1 + 6glox = 0 + -1 Reorder the terms: 1 + -1 + 30glo + 6glox = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 30glo + 6glox = 0 + -1 30glo + 6glox = 0 + -1 Combine like terms: 0 + -1 = -1 30glo + 6glox = -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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