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Simplifying Log[5](x + 4) + log[5](x + -4) = log[5] * 20 Reorder the terms: goL * 5(4 + x) + log[5](x + -4) = log[5] * 20 Reorder the terms for easier multiplication: 5goL(4 + x) + log[5](x + -4) = log[5] * 20 (4 * 5goL + x * 5goL) + log[5](x + -4) = log[5] * 20 (20goL + 5goxL) + log[5](x + -4) = log[5] * 20 Reorder the terms: 20goL + 5goxL + glo * 5(-4 + x) = log[5] * 20 Reorder the terms for easier multiplication: 20goL + 5goxL + 5glo(-4 + x) = log[5] * 20 20goL + 5goxL + (-4 * 5glo + x * 5glo) = log[5] * 20 20goL + 5goxL + (-20glo + 5glox) = log[5] * 20 Reorder the terms: -20glo + 5glox + 20goL + 5goxL = log[5] * 20 Reorder the terms for easier multiplication: -20glo + 5glox + 20goL + 5goxL = 5 * 20glo Multiply 5 * 20 -20glo + 5glox + 20goL + 5goxL = 100glo Solving -20glo + 5glox + 20goL + 5goxL = 100glo Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-100glo' to each side of the equation. -20glo + 5glox + 20goL + -100glo + 5goxL = 100glo + -100glo Reorder the terms: -20glo + -100glo + 5glox + 20goL + 5goxL = 100glo + -100glo Combine like terms: -20glo + -100glo = -120glo -120glo + 5glox + 20goL + 5goxL = 100glo + -100glo Combine like terms: 100glo + -100glo = 0 -120glo + 5glox + 20goL + 5goxL = 0 Factor out the Greatest Common Factor (GCF), '5go'. 5go(-24l + lx + 4L + xL) = 0 Ignore the factor 5.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 '(-24l + lx + 4L + xL)' equal to zero and attempt to solve: Simplifying -24l + lx + 4L + xL = 0 Reorder the terms: 4L + -24l + lx + xL = 0 Solving 4L + -24l + lx + xL = 0 Move all terms containing g to the left, all other terms to the right. Add '-4L' to each side of the equation. 4L + -24l + lx + -4L + xL = 0 + -4L Reorder the terms: 4L + -4L + -24l + lx + xL = 0 + -4L Combine like terms: 4L + -4L = 0 0 + -24l + lx + xL = 0 + -4L -24l + lx + xL = 0 + -4L Remove the zero: -24l + lx + xL = -4L Add '24l' to each side of the equation. -24l + lx + 24l + xL = -4L + 24l Reorder the terms: -24l + 24l + lx + xL = -4L + 24l Combine like terms: -24l + 24l = 0 0 + lx + xL = -4L + 24l lx + xL = -4L + 24l Add '-1lx' to each side of the equation. lx + -1lx + xL = -4L + 24l + -1lx Combine like terms: lx + -1lx = 0 0 + xL = -4L + 24l + -1lx xL = -4L + 24l + -1lx Add '-1xL' to each side of the equation. xL + -1xL = -4L + 24l + -1lx + -1xL Combine like terms: xL + -1xL = 0 0 = -4L + 24l + -1lx + -1xL Simplifying 0 = -4L + 24l + -1lx + -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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