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Simplifying Log[4] * x + -1log[4](x + 3) = log[4](x + -2) Reorder the terms for easier multiplication: 4goL * x + -1log[4](x + 3) = log[4](x + -2) Multiply goL * x 4goxL + -1log[4](x + 3) = log[4](x + -2) Reorder the terms: 4goxL + -1glo * 4(3 + x) = log[4](x + -2) Reorder the terms for easier multiplication: 4goxL + -1 * 4glo(3 + x) = log[4](x + -2) Multiply -1 * 4 4goxL + -4glo(3 + x) = log[4](x + -2) 4goxL + (3 * -4glo + x * -4glo) = log[4](x + -2) 4goxL + (-12glo + -4glox) = log[4](x + -2) Reorder the terms: -12glo + -4glox + 4goxL = log[4](x + -2) Reorder the terms: -12glo + -4glox + 4goxL = glo * 4(-2 + x) Reorder the terms for easier multiplication: -12glo + -4glox + 4goxL = 4glo(-2 + x) -12glo + -4glox + 4goxL = (-2 * 4glo + x * 4glo) -12glo + -4glox + 4goxL = (-8glo + 4glox) Solving -12glo + -4glox + 4goxL = -8glo + 4glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '8glo' to each side of the equation. -12glo + -4glox + 8glo + 4goxL = -8glo + 8glo + 4glox Reorder the terms: -12glo + 8glo + -4glox + 4goxL = -8glo + 8glo + 4glox Combine like terms: -12glo + 8glo = -4glo -4glo + -4glox + 4goxL = -8glo + 8glo + 4glox Combine like terms: -8glo + 8glo = 0 -4glo + -4glox + 4goxL = 0 + 4glox -4glo + -4glox + 4goxL = 4glox Add '-4glox' to each side of the equation. -4glo + -4glox + -4glox + 4goxL = 4glox + -4glox Combine like terms: -4glox + -4glox = -8glox -4glo + -8glox + 4goxL = 4glox + -4glox Combine like terms: 4glox + -4glox = 0 -4glo + -8glox + 4goxL = 0 Factor out the Greatest Common Factor (GCF), '4go'. 4go(-1l + -2lx + xL) = 0 Ignore the factor 4.Subproblem 1
Set the factor 'go' equal to zero and attempt to solve: Simplifying go = 0 Solving go = 0 Move all terms containing g to the left, all other terms to the right. Simplifying go = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(-1l + -2lx + xL)' equal to zero and attempt to solve: Simplifying -1l + -2lx + xL = 0 Solving -1l + -2lx + xL = 0 Move all terms containing g to the left, all other terms to the right. Add 'l' to each side of the equation. -1l + -2lx + l + xL = 0 + l Reorder the terms: -1l + l + -2lx + xL = 0 + l Combine like terms: -1l + l = 0 0 + -2lx + xL = 0 + l -2lx + xL = 0 + l Remove the zero: -2lx + xL = l Add '2lx' to each side of the equation. -2lx + 2lx + xL = l + 2lx Combine like terms: -2lx + 2lx = 0 0 + xL = l + 2lx xL = l + 2lx Add '-1xL' to each side of the equation. xL + -1xL = l + 2lx + -1xL Combine like terms: xL + -1xL = 0 0 = l + 2lx + -1xL Simplifying 0 = l + 2lx + -1xL 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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