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Simplifying log[4](3x + 2) = log[4](7) + -1log[4](3) Reorder the terms: glo * 4(2 + 3x) = log[4](7) + -1log[4](3) Reorder the terms for easier multiplication: 4glo(2 + 3x) = log[4](7) + -1log[4](3) (2 * 4glo + 3x * 4glo) = log[4](7) + -1log[4](3) (8glo + 12glox) = log[4](7) + -1log[4](3) Reorder the terms for easier multiplication: 8glo + 12glox = 4 * 7glo + -1log[4](3) Multiply 4 * 7 8glo + 12glox = 28glo + -1log[4](3) Reorder the terms for easier multiplication: 8glo + 12glox = 28glo + -1 * 4 * 3glo Multiply -1 * 4 8glo + 12glox = 28glo + -4 * 3glo Multiply -4 * 3 8glo + 12glox = 28glo + -12glo Combine like terms: 28glo + -12glo = 16glo 8glo + 12glox = 16glo Solving 8glo + 12glox = 16glo Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-16glo' to each side of the equation. 8glo + -16glo + 12glox = 16glo + -16glo Combine like terms: 8glo + -16glo = -8glo -8glo + 12glox = 16glo + -16glo Combine like terms: 16glo + -16glo = 0 -8glo + 12glox = 0 Factor out the Greatest Common Factor (GCF), '4glo'. 4glo(-2 + 3x) = 0 Ignore the factor 4.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 + 3x)' equal to zero and attempt to solve: Simplifying -2 + 3x = 0 Solving -2 + 3x = 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 + 3x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 3x = 0 + 2 3x = 0 + 2 Combine like terms: 0 + 2 = 2 3x = 2 Add '-3x' to each side of the equation. 3x + -3x = 2 + -3x Combine like terms: 3x + -3x = 0 0 = 2 + -3x Simplifying 0 = 2 + -3x 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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