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Simplifying log(5x + 2) + log(2) = log(9x + 10) Reorder the terms: glo(2 + 5x) + log(2) = log(9x + 10) (2 * glo + 5x * glo) + log(2) = log(9x + 10) (2glo + 5glox) + log(2) = log(9x + 10) Reorder the terms for easier multiplication: 2glo + 5glox + 2glo = log(9x + 10) Reorder the terms: 2glo + 2glo + 5glox = log(9x + 10) Combine like terms: 2glo + 2glo = 4glo 4glo + 5glox = log(9x + 10) Reorder the terms: 4glo + 5glox = glo(10 + 9x) 4glo + 5glox = (10 * glo + 9x * glo) 4glo + 5glox = (10glo + 9glox) Solving 4glo + 5glox = 10glo + 9glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-10glo' to each side of the equation. 4glo + -10glo + 5glox = 10glo + -10glo + 9glox Combine like terms: 4glo + -10glo = -6glo -6glo + 5glox = 10glo + -10glo + 9glox Combine like terms: 10glo + -10glo = 0 -6glo + 5glox = 0 + 9glox -6glo + 5glox = 9glox Add '-9glox' to each side of the equation. -6glo + 5glox + -9glox = 9glox + -9glox Combine like terms: 5glox + -9glox = -4glox -6glo + -4glox = 9glox + -9glox Combine like terms: 9glox + -9glox = 0 -6glo + -4glox = 0 Factor out the Greatest Common Factor (GCF), '-2glo'. -2glo(3 + 2x) = 0 Ignore the factor -2.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 '(3 + 2x)' equal to zero and attempt to solve: Simplifying 3 + 2x = 0 Solving 3 + 2x = 0 Move all terms containing g to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + 2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2x = 0 + -3 2x = 0 + -3 Combine like terms: 0 + -3 = -3 2x = -3 Add '-2x' to each side of the equation. 2x + -2x = -3 + -2x Combine like terms: 2x + -2x = 0 0 = -3 + -2x Simplifying 0 = -3 + -2x 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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