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Simplifying Log(2)(4x + -8) + -1log(2)(x + 5) = 4 Reorder the terms: goL * 2(-8 + 4x) + -1log(2)(x + 5) = 4 Reorder the terms for easier multiplication: 2goL(-8 + 4x) + -1log(2)(x + 5) = 4 (-8 * 2goL + 4x * 2goL) + -1log(2)(x + 5) = 4 (-16goL + 8goxL) + -1log(2)(x + 5) = 4 Reorder the terms: -16goL + 8goxL + -1glo * 2(5 + x) = 4 Reorder the terms for easier multiplication: -16goL + 8goxL + -1 * 2glo(5 + x) = 4 Multiply -1 * 2 -16goL + 8goxL + -2glo(5 + x) = 4 -16goL + 8goxL + (5 * -2glo + x * -2glo) = 4 -16goL + 8goxL + (-10glo + -2glox) = 4 Reorder the terms: -10glo + -2glox + -16goL + 8goxL = 4 Solving -10glo + -2glox + -16goL + 8goxL = 4 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Reorder the terms: -4 + -10glo + -2glox + -16goL + 8goxL = 4 + -4 Combine like terms: 4 + -4 = 0 -4 + -10glo + -2glox + -16goL + 8goxL = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-2 + -5glo + -1glox + -8goL + 4goxL) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-2 + -5glo + -1glox + -8goL + 4goxL)' equal to zero and attempt to solve: Simplifying -2 + -5glo + -1glox + -8goL + 4goxL = 0 Solving -2 + -5glo + -1glox + -8goL + 4goxL = 0 Move all terms containing g to the left, all other terms to the right. Add '2' to each side of the equation. -2 + -5glo + -1glox + -8goL + 2 + 4goxL = 0 + 2 Reorder the terms: -2 + 2 + -5glo + -1glox + -8goL + 4goxL = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -5glo + -1glox + -8goL + 4goxL = 0 + 2 -5glo + -1glox + -8goL + 4goxL = 0 + 2 Combine like terms: 0 + 2 = 2 -5glo + -1glox + -8goL + 4goxL = 2 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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