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