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Simplifying log[4](x + -2) = log[4](3x + 7) Reorder the terms: glo * 4(-2 + x) = log[4](3x + 7) Reorder the terms for easier multiplication: 4glo(-2 + x) = log[4](3x + 7) (-2 * 4glo + x * 4glo) = log[4](3x + 7) (-8glo + 4glox) = log[4](3x + 7) Reorder the terms: -8glo + 4glox = glo * 4(7 + 3x) Reorder the terms for easier multiplication: -8glo + 4glox = 4glo(7 + 3x) -8glo + 4glox = (7 * 4glo + 3x * 4glo) -8glo + 4glox = (28glo + 12glox) Solving -8glo + 4glox = 28glo + 12glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-28glo' to each side of the equation. -8glo + -28glo + 4glox = 28glo + -28glo + 12glox Combine like terms: -8glo + -28glo = -36glo -36glo + 4glox = 28glo + -28glo + 12glox Combine like terms: 28glo + -28glo = 0 -36glo + 4glox = 0 + 12glox -36glo + 4glox = 12glox Add '-12glox' to each side of the equation. -36glo + 4glox + -12glox = 12glox + -12glox Combine like terms: 4glox + -12glox = -8glox -36glo + -8glox = 12glox + -12glox Combine like terms: 12glox + -12glox = 0 -36glo + -8glox = 0 Factor out the Greatest Common Factor (GCF), '-4glo'. -4glo(9 + 2x) = 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 '(9 + 2x)' equal to zero and attempt to solve: Simplifying 9 + 2x = 0 Solving 9 + 2x = 0 Move all terms containing g to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + 2x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 2x = 0 + -9 2x = 0 + -9 Combine like terms: 0 + -9 = -9 2x = -9 Add '-2x' to each side of the equation. 2x + -2x = -9 + -2x Combine like terms: 2x + -2x = 0 0 = -9 + -2x Simplifying 0 = -9 + -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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