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Simplifying log(3)(4x + 5) + -1log(3)(6x + -3) = log(3)(7) Reorder the terms: glo * 3(5 + 4x) + -1log(3)(6x + -3) = log(3)(7) Reorder the terms for easier multiplication: 3glo(5 + 4x) + -1log(3)(6x + -3) = log(3)(7) (5 * 3glo + 4x * 3glo) + -1log(3)(6x + -3) = log(3)(7) (15glo + 12glox) + -1log(3)(6x + -3) = log(3)(7) Reorder the terms: 15glo + 12glox + -1glo * 3(-3 + 6x) = log(3)(7) Reorder the terms for easier multiplication: 15glo + 12glox + -1 * 3glo(-3 + 6x) = log(3)(7) Multiply -1 * 3 15glo + 12glox + -3glo(-3 + 6x) = log(3)(7) 15glo + 12glox + (-3 * -3glo + 6x * -3glo) = log(3)(7) 15glo + 12glox + (9glo + -18glox) = log(3)(7) Reorder the terms: 15glo + 9glo + 12glox + -18glox = log(3)(7) Combine like terms: 15glo + 9glo = 24glo 24glo + 12glox + -18glox = log(3)(7) Combine like terms: 12glox + -18glox = -6glox 24glo + -6glox = log(3)(7) Reorder the terms for easier multiplication: 24glo + -6glox = 3 * 7glo Multiply 3 * 7 24glo + -6glox = 21glo Solving 24glo + -6glox = 21glo Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-21glo' to each side of the equation. 24glo + -21glo + -6glox = 21glo + -21glo Combine like terms: 24glo + -21glo = 3glo 3glo + -6glox = 21glo + -21glo Combine like terms: 21glo + -21glo = 0 3glo + -6glox = 0 Factor out the Greatest Common Factor (GCF), '3glo'. 3glo(1 + -2x) = 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 '(1 + -2x)' equal to zero and attempt to solve: Simplifying 1 + -2x = 0 Solving 1 + -2x = 0 Move all terms containing g to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2x = 0 + -1 -2x = 0 + -1 Combine like terms: 0 + -1 = -1 -2x = -1 Add '2x' to each side of the equation. -2x + 2x = -1 + 2x Combine like terms: -2x + 2x = 0 0 = -1 + 2x Simplifying 0 = -1 + 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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