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Simplifying Log[4](x + -7) + -1log[4](x + -4) = 2 Reorder the terms: goL * 4(-7 + x) + -1log[4](x + -4) = 2 Reorder the terms for easier multiplication: 4goL(-7 + x) + -1log[4](x + -4) = 2 (-7 * 4goL + x * 4goL) + -1log[4](x + -4) = 2 (-28goL + 4goxL) + -1log[4](x + -4) = 2 Reorder the terms: -28goL + 4goxL + -1glo * 4(-4 + x) = 2 Reorder the terms for easier multiplication: -28goL + 4goxL + -1 * 4glo(-4 + x) = 2 Multiply -1 * 4 -28goL + 4goxL + -4glo(-4 + x) = 2 -28goL + 4goxL + (-4 * -4glo + x * -4glo) = 2 -28goL + 4goxL + (16glo + -4glox) = 2 Reorder the terms: 16glo + -4glox + -28goL + 4goxL = 2 Solving 16glo + -4glox + -28goL + 4goxL = 2 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Reorder the terms: -2 + 16glo + -4glox + -28goL + 4goxL = 2 + -2 Combine like terms: 2 + -2 = 0 -2 + 16glo + -4glox + -28goL + 4goxL = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-1 + 8glo + -2glox + -14goL + 2goxL) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + 8glo + -2glox + -14goL + 2goxL)' equal to zero and attempt to solve: Simplifying -1 + 8glo + -2glox + -14goL + 2goxL = 0 Solving -1 + 8glo + -2glox + -14goL + 2goxL = 0 Move all terms containing g to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 8glo + -2glox + -14goL + 1 + 2goxL = 0 + 1 Reorder the terms: -1 + 1 + 8glo + -2glox + -14goL + 2goxL = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 8glo + -2glox + -14goL + 2goxL = 0 + 1 8glo + -2glox + -14goL + 2goxL = 0 + 1 Combine like terms: 0 + 1 = 1 8glo + -2glox + -14goL + 2goxL = 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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