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Simplifying log[4] * x + log[4](5x + -4) = log[4](2x + -5) Reorder the terms for easier multiplication: 4glo * x + log[4](5x + -4) = log[4](2x + -5) Multiply glo * x 4glox + log[4](5x + -4) = log[4](2x + -5) Reorder the terms: 4glox + glo * 4(-4 + 5x) = log[4](2x + -5) Reorder the terms for easier multiplication: 4glox + 4glo(-4 + 5x) = log[4](2x + -5) 4glox + (-4 * 4glo + 5x * 4glo) = log[4](2x + -5) 4glox + (-16glo + 20glox) = log[4](2x + -5) Reorder the terms: -16glo + 4glox + 20glox = log[4](2x + -5) Combine like terms: 4glox + 20glox = 24glox -16glo + 24glox = log[4](2x + -5) Reorder the terms: -16glo + 24glox = glo * 4(-5 + 2x) Reorder the terms for easier multiplication: -16glo + 24glox = 4glo(-5 + 2x) -16glo + 24glox = (-5 * 4glo + 2x * 4glo) -16glo + 24glox = (-20glo + 8glox) Solving -16glo + 24glox = -20glo + 8glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '20glo' to each side of the equation. -16glo + 20glo + 24glox = -20glo + 20glo + 8glox Combine like terms: -16glo + 20glo = 4glo 4glo + 24glox = -20glo + 20glo + 8glox Combine like terms: -20glo + 20glo = 0 4glo + 24glox = 0 + 8glox 4glo + 24glox = 8glox Add '-8glox' to each side of the equation. 4glo + 24glox + -8glox = 8glox + -8glox Combine like terms: 24glox + -8glox = 16glox 4glo + 16glox = 8glox + -8glox Combine like terms: 8glox + -8glox = 0 4glo + 16glox = 0 Factor out the Greatest Common Factor (GCF), '4glo'. 4glo(1 + 4x) = 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 '(1 + 4x)' equal to zero and attempt to solve: Simplifying 1 + 4x = 0 Solving 1 + 4x = 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 + 4x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 4x = 0 + -1 4x = 0 + -1 Combine like terms: 0 + -1 = -1 4x = -1 Add '-4x' to each side of the equation. 4x + -4x = -1 + -4x Combine like terms: 4x + -4x = 0 0 = -1 + -4x Simplifying 0 = -1 + -4x 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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