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Simplifying log[4](2x) = log[4](3x + 14) Remove parenthesis around (2x) glo * 4 * 2x = log[4](3x + 14) Reorder the terms for easier multiplication: 4 * 2glo * x = log[4](3x + 14) Multiply 4 * 2 8glo * x = log[4](3x + 14) Multiply glo * x 8glox = log[4](3x + 14) Reorder the terms: 8glox = glo * 4(14 + 3x) Reorder the terms for easier multiplication: 8glox = 4glo(14 + 3x) 8glox = (14 * 4glo + 3x * 4glo) 8glox = (56glo + 12glox) Solving 8glox = 56glo + 12glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-56glo' to each side of the equation. -56glo + 8glox = 56glo + -56glo + 12glox Combine like terms: 56glo + -56glo = 0 -56glo + 8glox = 0 + 12glox -56glo + 8glox = 12glox Add '-12glox' to each side of the equation. -56glo + 8glox + -12glox = 12glox + -12glox Combine like terms: 8glox + -12glox = -4glox -56glo + -4glox = 12glox + -12glox Combine like terms: 12glox + -12glox = 0 -56glo + -4glox = 0 Factor out the Greatest Common Factor (GCF), '-4glo'. -4glo(14 + x) = 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 '(14 + x)' equal to zero and attempt to solve: Simplifying 14 + x = 0 Solving 14 + x = 0 Move all terms containing g to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + x = 0 + -14 Combine like terms: 14 + -14 = 0 0 + x = 0 + -14 x = 0 + -14 Combine like terms: 0 + -14 = -14 x = -14 Add '-1x' to each side of the equation. x + -1x = -14 + -1x Combine like terms: x + -1x = 0 0 = -14 + -1x Simplifying 0 = -14 + -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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