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Simplifying log[4](2x + 6) + -1log[4](x + -4) = 2 Reorder the terms: glo * 4(6 + 2x) + -1log[4](x + -4) = 2 Reorder the terms for easier multiplication: 4glo(6 + 2x) + -1log[4](x + -4) = 2 (6 * 4glo + 2x * 4glo) + -1log[4](x + -4) = 2 (24glo + 8glox) + -1log[4](x + -4) = 2 Reorder the terms: 24glo + 8glox + -1glo * 4(-4 + x) = 2 Reorder the terms for easier multiplication: 24glo + 8glox + -1 * 4glo(-4 + x) = 2 Multiply -1 * 4 24glo + 8glox + -4glo(-4 + x) = 2 24glo + 8glox + (-4 * -4glo + x * -4glo) = 2 24glo + 8glox + (16glo + -4glox) = 2 Reorder the terms: 24glo + 16glo + 8glox + -4glox = 2 Combine like terms: 24glo + 16glo = 40glo 40glo + 8glox + -4glox = 2 Combine like terms: 8glox + -4glox = 4glox 40glo + 4glox = 2 Solving 40glo + 4glox = 2 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Reorder the terms: -2 + 40glo + 4glox = 2 + -2 Combine like terms: 2 + -2 = 0 -2 + 40glo + 4glox = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-1 + 20glo + 2glox) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + 20glo + 2glox)' equal to zero and attempt to solve: Simplifying -1 + 20glo + 2glox = 0 Solving -1 + 20glo + 2glox = 0 Move all terms containing g to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 20glo + 1 + 2glox = 0 + 1 Reorder the terms: -1 + 1 + 20glo + 2glox = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 20glo + 2glox = 0 + 1 20glo + 2glox = 0 + 1 Combine like terms: 0 + 1 = 1 20glo + 2glox = 1 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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