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Simplifying log[4](3x + 2) = log[4](5) + log[4](3) Reorder the terms: glo * 4(2 + 3x) = log[4](5) + log[4](3) Reorder the terms for easier multiplication: 4glo(2 + 3x) = log[4](5) + log[4](3) (2 * 4glo + 3x * 4glo) = log[4](5) + log[4](3) (8glo + 12glox) = log[4](5) + log[4](3) Reorder the terms for easier multiplication: 8glo + 12glox = 4 * 5glo + log[4](3) Multiply 4 * 5 8glo + 12glox = 20glo + log[4](3) Reorder the terms for easier multiplication: 8glo + 12glox = 20glo + 4 * 3glo Multiply 4 * 3 8glo + 12glox = 20glo + 12glo Combine like terms: 20glo + 12glo = 32glo 8glo + 12glox = 32glo Solving 8glo + 12glox = 32glo Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-32glo' to each side of the equation. 8glo + -32glo + 12glox = 32glo + -32glo Combine like terms: 8glo + -32glo = -24glo -24glo + 12glox = 32glo + -32glo Combine like terms: 32glo + -32glo = 0 -24glo + 12glox = 0 Factor out the Greatest Common Factor (GCF), '12glo'. 12glo(-2 + x) = 0 Ignore the factor 12.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 '(-2 + x)' equal to zero and attempt to solve: Simplifying -2 + x = 0 Solving -2 + x = 0 Move all terms containing g to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + x = 0 + 2 x = 0 + 2 Combine like terms: 0 + 2 = 2 x = 2 Add '-1x' to each side of the equation. x + -1x = 2 + -1x Combine like terms: x + -1x = 0 0 = 2 + -1x Simplifying 0 = 2 + -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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