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Simplifying Log[5](4x + -7) = log[5](x + 5) Reorder the terms: goL * 5(-7 + 4x) = log[5](x + 5) Reorder the terms for easier multiplication: 5goL(-7 + 4x) = log[5](x + 5) (-7 * 5goL + 4x * 5goL) = log[5](x + 5) (-35goL + 20goxL) = log[5](x + 5) Reorder the terms: -35goL + 20goxL = glo * 5(5 + x) Reorder the terms for easier multiplication: -35goL + 20goxL = 5glo(5 + x) -35goL + 20goxL = (5 * 5glo + x * 5glo) -35goL + 20goxL = (25glo + 5glox) Solving -35goL + 20goxL = 25glo + 5glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-25glo' to each side of the equation. -35goL + -25glo + 20goxL = 25glo + -25glo + 5glox Reorder the terms: -25glo + -35goL + 20goxL = 25glo + -25glo + 5glox Combine like terms: 25glo + -25glo = 0 -25glo + -35goL + 20goxL = 0 + 5glox -25glo + -35goL + 20goxL = 5glox Add '-5glox' to each side of the equation. -25glo + -35goL + -5glox + 20goxL = 5glox + -5glox Reorder the terms: -25glo + -5glox + -35goL + 20goxL = 5glox + -5glox Combine like terms: 5glox + -5glox = 0 -25glo + -5glox + -35goL + 20goxL = 0 Factor out the Greatest Common Factor (GCF), '5go'. 5go(-5l + -1lx + -7L + 4xL) = 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 '(-5l + -1lx + -7L + 4xL)' equal to zero and attempt to solve: Simplifying -5l + -1lx + -7L + 4xL = 0 Reorder the terms: -7L + -5l + -1lx + 4xL = 0 Solving -7L + -5l + -1lx + 4xL = 0 Move all terms containing g to the left, all other terms to the right. Add '7L' to each side of the equation. -7L + -5l + -1lx + 7L + 4xL = 0 + 7L Reorder the terms: -7L + 7L + -5l + -1lx + 4xL = 0 + 7L Combine like terms: -7L + 7L = 0 0 + -5l + -1lx + 4xL = 0 + 7L -5l + -1lx + 4xL = 0 + 7L Remove the zero: -5l + -1lx + 4xL = 7L Add '5l' to each side of the equation. -5l + -1lx + 5l + 4xL = 7L + 5l Reorder the terms: -5l + 5l + -1lx + 4xL = 7L + 5l Combine like terms: -5l + 5l = 0 0 + -1lx + 4xL = 7L + 5l -1lx + 4xL = 7L + 5l Add 'lx' to each side of the equation. -1lx + lx + 4xL = 7L + 5l + lx Combine like terms: -1lx + lx = 0 0 + 4xL = 7L + 5l + lx 4xL = 7L + 5l + lx Add '-4xL' to each side of the equation. 4xL + -4xL = 7L + 5l + lx + -4xL Combine like terms: 4xL + -4xL = 0 0 = 7L + 5l + lx + -4xL Simplifying 0 = 7L + 5l + lx + -4xL 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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