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Simplifying log(3) * x = log(9)(7x + 18) Reorder the terms for easier multiplication: 3glo * x = log(9)(7x + 18) Multiply glo * x 3glox = log(9)(7x + 18) Reorder the terms: 3glox = glo * 9(18 + 7x) Reorder the terms for easier multiplication: 3glox = 9glo(18 + 7x) 3glox = (18 * 9glo + 7x * 9glo) 3glox = (162glo + 63glox) Solving 3glox = 162glo + 63glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-162glo' to each side of the equation. -162glo + 3glox = 162glo + -162glo + 63glox Combine like terms: 162glo + -162glo = 0 -162glo + 3glox = 0 + 63glox -162glo + 3glox = 63glox Add '-63glox' to each side of the equation. -162glo + 3glox + -63glox = 63glox + -63glox Combine like terms: 3glox + -63glox = -60glox -162glo + -60glox = 63glox + -63glox Combine like terms: 63glox + -63glox = 0 -162glo + -60glox = 0 Factor out the Greatest Common Factor (GCF), '-6glo'. -6glo(27 + 10x) = 0 Ignore the factor -6.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 '(27 + 10x)' equal to zero and attempt to solve: Simplifying 27 + 10x = 0 Solving 27 + 10x = 0 Move all terms containing g to the left, all other terms to the right. Add '-27' to each side of the equation. 27 + -27 + 10x = 0 + -27 Combine like terms: 27 + -27 = 0 0 + 10x = 0 + -27 10x = 0 + -27 Combine like terms: 0 + -27 = -27 10x = -27 Add '-10x' to each side of the equation. 10x + -10x = -27 + -10x Combine like terms: 10x + -10x = 0 0 = -27 + -10x Simplifying 0 = -27 + -10x 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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