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Simplifying log(5x + 3) + log(2) = log(9x + 10) Reorder the terms: glo(3 + 5x) + log(2) = log(9x + 10) (3 * glo + 5x * glo) + log(2) = log(9x + 10) (3glo + 5glox) + log(2) = log(9x + 10) Reorder the terms for easier multiplication: 3glo + 5glox + 2glo = log(9x + 10) Reorder the terms: 3glo + 2glo + 5glox = log(9x + 10) Combine like terms: 3glo + 2glo = 5glo 5glo + 5glox = log(9x + 10) Reorder the terms: 5glo + 5glox = glo(10 + 9x) 5glo + 5glox = (10 * glo + 9x * glo) 5glo + 5glox = (10glo + 9glox) Solving 5glo + 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. 5glo + -10glo + 5glox = 10glo + -10glo + 9glox Combine like terms: 5glo + -10glo = -5glo -5glo + 5glox = 10glo + -10glo + 9glox Combine like terms: 10glo + -10glo = 0 -5glo + 5glox = 0 + 9glox -5glo + 5glox = 9glox Add '-9glox' to each side of the equation. -5glo + 5glox + -9glox = 9glox + -9glox Combine like terms: 5glox + -9glox = -4glox -5glo + -4glox = 9glox + -9glox Combine like terms: 9glox + -9glox = 0 -5glo + -4glox = 0 Factor out the Greatest Common Factor (GCF), '-1glo'. -1glo(5 + 4x) = 0 Ignore the factor -1.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 '(5 + 4x)' equal to zero and attempt to solve: Simplifying 5 + 4x = 0 Solving 5 + 4x = 0 Move all terms containing g to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 4x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 4x = 0 + -5 4x = 0 + -5 Combine like terms: 0 + -5 = -5 4x = -5 Add '-4x' to each side of the equation. 4x + -4x = -5 + -4x Combine like terms: 4x + -4x = 0 0 = -5 + -4x Simplifying 0 = -5 + -4x 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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