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Simplifying log(3)(2x + -7) = log(3)(3x + 38) Reorder the terms: glo * 3(-7 + 2x) = log(3)(3x + 38) Reorder the terms for easier multiplication: 3glo(-7 + 2x) = log(3)(3x + 38) (-7 * 3glo + 2x * 3glo) = log(3)(3x + 38) (-21glo + 6glox) = log(3)(3x + 38) Reorder the terms: -21glo + 6glox = glo * 3(38 + 3x) Reorder the terms for easier multiplication: -21glo + 6glox = 3glo(38 + 3x) -21glo + 6glox = (38 * 3glo + 3x * 3glo) -21glo + 6glox = (114glo + 9glox) Solving -21glo + 6glox = 114glo + 9glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-114glo' to each side of the equation. -21glo + -114glo + 6glox = 114glo + -114glo + 9glox Combine like terms: -21glo + -114glo = -135glo -135glo + 6glox = 114glo + -114glo + 9glox Combine like terms: 114glo + -114glo = 0 -135glo + 6glox = 0 + 9glox -135glo + 6glox = 9glox Add '-9glox' to each side of the equation. -135glo + 6glox + -9glox = 9glox + -9glox Combine like terms: 6glox + -9glox = -3glox -135glo + -3glox = 9glox + -9glox Combine like terms: 9glox + -9glox = 0 -135glo + -3glox = 0 Factor out the Greatest Common Factor (GCF), '-3glo'. -3glo(45 + x) = 0 Ignore the factor -3.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 '(45 + x)' equal to zero and attempt to solve: Simplifying 45 + x = 0 Solving 45 + x = 0 Move all terms containing g to the left, all other terms to the right. Add '-45' to each side of the equation. 45 + -45 + x = 0 + -45 Combine like terms: 45 + -45 = 0 0 + x = 0 + -45 x = 0 + -45 Combine like terms: 0 + -45 = -45 x = -45 Add '-1x' to each side of the equation. x + -1x = -45 + -1x Combine like terms: x + -1x = 0 0 = -45 + -1x Simplifying 0 = -45 + -1x 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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