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Simplifying log[5](9x + -5) + -1log[5](x + -3) = 2 Reorder the terms: glo * 5(-5 + 9x) + -1log[5](x + -3) = 2 Reorder the terms for easier multiplication: 5glo(-5 + 9x) + -1log[5](x + -3) = 2 (-5 * 5glo + 9x * 5glo) + -1log[5](x + -3) = 2 (-25glo + 45glox) + -1log[5](x + -3) = 2 Reorder the terms: -25glo + 45glox + -1glo * 5(-3 + x) = 2 Reorder the terms for easier multiplication: -25glo + 45glox + -1 * 5glo(-3 + x) = 2 Multiply -1 * 5 -25glo + 45glox + -5glo(-3 + x) = 2 -25glo + 45glox + (-3 * -5glo + x * -5glo) = 2 -25glo + 45glox + (15glo + -5glox) = 2 Reorder the terms: -25glo + 15glo + 45glox + -5glox = 2 Combine like terms: -25glo + 15glo = -10glo -10glo + 45glox + -5glox = 2 Combine like terms: 45glox + -5glox = 40glox -10glo + 40glox = 2 Solving -10glo + 40glox = 2 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Reorder the terms: -2 + -10glo + 40glox = 2 + -2 Combine like terms: 2 + -2 = 0 -2 + -10glo + 40glox = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-1 + -5glo + 20glox) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + -5glo + 20glox)' equal to zero and attempt to solve: Simplifying -1 + -5glo + 20glox = 0 Solving -1 + -5glo + 20glox = 0 Move all terms containing g to the left, all other terms to the right. Add '1' to each side of the equation. -1 + -5glo + 1 + 20glox = 0 + 1 Reorder the terms: -1 + 1 + -5glo + 20glox = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -5glo + 20glox = 0 + 1 -5glo + 20glox = 0 + 1 Combine like terms: 0 + 1 = 1 -5glo + 20glox = 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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