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Simplifying log[4](4x + 14) + -1log[4](x2 + 3x + -17) = 2 Reorder the terms: glo * 4(14 + 4x) + -1log[4](x2 + 3x + -17) = 2 Reorder the terms for easier multiplication: 4glo(14 + 4x) + -1log[4](x2 + 3x + -17) = 2 (14 * 4glo + 4x * 4glo) + -1log[4](x2 + 3x + -17) = 2 (56glo + 16glox) + -1log[4](x2 + 3x + -17) = 2 Reorder the terms: 56glo + 16glox + -1glo * 4(-17 + 3x + x2) = 2 Reorder the terms for easier multiplication: 56glo + 16glox + -1 * 4glo(-17 + 3x + x2) = 2 Multiply -1 * 4 56glo + 16glox + -4glo(-17 + 3x + x2) = 2 56glo + 16glox + (-17 * -4glo + 3x * -4glo + x2 * -4glo) = 2 56glo + 16glox + (68glo + -12glox + -4glox2) = 2 Reorder the terms: 56glo + 68glo + 16glox + -12glox + -4glox2 = 2 Combine like terms: 56glo + 68glo = 124glo 124glo + 16glox + -12glox + -4glox2 = 2 Combine like terms: 16glox + -12glox = 4glox 124glo + 4glox + -4glox2 = 2 Solving 124glo + 4glox + -4glox2 = 2 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Reorder the terms: -2 + 124glo + 4glox + -4glox2 = 2 + -2 Combine like terms: 2 + -2 = 0 -2 + 124glo + 4glox + -4glox2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-1 + 62glo + 2glox + -2glox2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + 62glo + 2glox + -2glox2)' equal to zero and attempt to solve: Simplifying -1 + 62glo + 2glox + -2glox2 = 0 Solving -1 + 62glo + 2glox + -2glox2 = 0 Move all terms containing g to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 62glo + 2glox + 1 + -2glox2 = 0 + 1 Reorder the terms: -1 + 1 + 62glo + 2glox + -2glox2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 62glo + 2glox + -2glox2 = 0 + 1 62glo + 2glox + -2glox2 = 0 + 1 Combine like terms: 0 + 1 = 1 62glo + 2glox + -2glox2 = 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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