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Simplifying log(5)(5x + 9) = log(5)(6x) Reorder the terms: glo * 5(9 + 5x) = log(5)(6x) Reorder the terms for easier multiplication: 5glo(9 + 5x) = log(5)(6x) (9 * 5glo + 5x * 5glo) = log(5)(6x) (45glo + 25glox) = log(5)(6x) Remove parenthesis around (6x) 45glo + 25glox = glo * 5 * 6x Reorder the terms for easier multiplication: 45glo + 25glox = 5 * 6glo * x Multiply 5 * 6 45glo + 25glox = 30glo * x Multiply glo * x 45glo + 25glox = 30glox Solving 45glo + 25glox = 30glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-30glox' to each side of the equation. 45glo + 25glox + -30glox = 30glox + -30glox Combine like terms: 25glox + -30glox = -5glox 45glo + -5glox = 30glox + -30glox Combine like terms: 30glox + -30glox = 0 45glo + -5glox = 0 Factor out the Greatest Common Factor (GCF), '5glo'. 5glo(9 + -1x) = 0 Ignore the factor 5.Subproblem 1
Set the factor 'glo' equal to zero and attempt to solve: Simplifying glo = 0 Solving glo = 0 Move all terms containing g to the left, all other terms to the right. Simplifying glo = 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 '(9 + -1x)' equal to zero and attempt to solve: Simplifying 9 + -1x = 0 Solving 9 + -1x = 0 Move all terms containing g to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -1x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1x = 0 + -9 -1x = 0 + -9 Combine like terms: 0 + -9 = -9 -1x = -9 Add 'x' to each side of the equation. -1x + x = -9 + x Combine like terms: -1x + x = 0 0 = -9 + x Simplifying 0 = -9 + x 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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