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Simplifying log[4](2x + -5) = log[4](x + 5) Reorder the terms: glo * 4(-5 + 2x) = log[4](x + 5) Reorder the terms for easier multiplication: 4glo(-5 + 2x) = log[4](x + 5) (-5 * 4glo + 2x * 4glo) = log[4](x + 5) (-20glo + 8glox) = log[4](x + 5) Reorder the terms: -20glo + 8glox = glo * 4(5 + x) Reorder the terms for easier multiplication: -20glo + 8glox = 4glo(5 + x) -20glo + 8glox = (5 * 4glo + x * 4glo) -20glo + 8glox = (20glo + 4glox) Solving -20glo + 8glox = 20glo + 4glox 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. -20glo + -20glo + 8glox = 20glo + -20glo + 4glox Combine like terms: -20glo + -20glo = -40glo -40glo + 8glox = 20glo + -20glo + 4glox Combine like terms: 20glo + -20glo = 0 -40glo + 8glox = 0 + 4glox -40glo + 8glox = 4glox Add '-4glox' to each side of the equation. -40glo + 8glox + -4glox = 4glox + -4glox Combine like terms: 8glox + -4glox = 4glox -40glo + 4glox = 4glox + -4glox Combine like terms: 4glox + -4glox = 0 -40glo + 4glox = 0 Factor out the Greatest Common Factor (GCF), '4glo'. 4glo(-10 + 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 '(-10 + x)' equal to zero and attempt to solve: Simplifying -10 + x = 0 Solving -10 + x = 0 Move all terms containing g to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = 0 + 10 Combine like terms: -10 + 10 = 0 0 + x = 0 + 10 x = 0 + 10 Combine like terms: 0 + 10 = 10 x = 10 Add '-1x' to each side of the equation. x + -1x = 10 + -1x Combine like terms: x + -1x = 0 0 = 10 + -1x Simplifying 0 = 10 + -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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