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Simplifying log[4](4x + 3) + -1log[4](x + -3) + -2 = 0 Reorder the terms: glo * 4(3 + 4x) + -1log[4](x + -3) + -2 = 0 Reorder the terms for easier multiplication: 4glo(3 + 4x) + -1log[4](x + -3) + -2 = 0 (3 * 4glo + 4x * 4glo) + -1log[4](x + -3) + -2 = 0 (12glo + 16glox) + -1log[4](x + -3) + -2 = 0 Reorder the terms: 12glo + 16glox + -1glo * 4(-3 + x) + -2 = 0 Reorder the terms for easier multiplication: 12glo + 16glox + -1 * 4glo(-3 + x) + -2 = 0 Multiply -1 * 4 12glo + 16glox + -4glo(-3 + x) + -2 = 0 12glo + 16glox + (-3 * -4glo + x * -4glo) + -2 = 0 12glo + 16glox + (12glo + -4glox) + -2 = 0 Reorder the terms: -2 + 12glo + 12glo + 16glox + -4glox = 0 Combine like terms: 12glo + 12glo = 24glo -2 + 24glo + 16glox + -4glox = 0 Combine like terms: 16glox + -4glox = 12glox -2 + 24glo + 12glox = 0 Solving -2 + 24glo + 12glox = 0 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 24glo + 2 + 12glox = 0 + 2 Reorder the terms: -2 + 2 + 24glo + 12glox = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 24glo + 12glox = 0 + 2 24glo + 12glox = 0 + 2 Combine like terms: 0 + 2 = 2 24glo + 12glox = 2 Reorder the terms: -2 + 24glo + 12glox = 2 + -2 Combine like terms: 2 + -2 = 0 -2 + 24glo + 12glox = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-1 + 12glo + 6glox) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + 12glo + 6glox)' equal to zero and attempt to solve: Simplifying -1 + 12glo + 6glox = 0 Solving -1 + 12glo + 6glox = 0 Move all terms containing g to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 12glo + 1 + 6glox = 0 + 1 Reorder the terms: -1 + 1 + 12glo + 6glox = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 12glo + 6glox = 0 + 1 12glo + 6glox = 0 + 1 Combine like terms: 0 + 1 = 1 12glo + 6glox = 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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