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Simplifying log[5](y2 + 5y + 16) = log[5](y + 3) + log[5] * 4 Reorder the terms: glo * 5(16 + 5y + y2) = log[5](y + 3) + log[5] * 4 Reorder the terms for easier multiplication: 5glo(16 + 5y + y2) = log[5](y + 3) + log[5] * 4 (16 * 5glo + 5y * 5glo + y2 * 5glo) = log[5](y + 3) + log[5] * 4 (80glo + 25gloy + 5gloy2) = log[5](y + 3) + log[5] * 4 Reorder the terms: 80glo + 25gloy + 5gloy2 = glo * 5(3 + y) + log[5] * 4 Reorder the terms for easier multiplication: 80glo + 25gloy + 5gloy2 = 5glo(3 + y) + log[5] * 4 80glo + 25gloy + 5gloy2 = (3 * 5glo + y * 5glo) + log[5] * 4 80glo + 25gloy + 5gloy2 = (15glo + 5gloy) + log[5] * 4 Reorder the terms for easier multiplication: 80glo + 25gloy + 5gloy2 = 15glo + 5gloy + 5 * 4glo Multiply 5 * 4 80glo + 25gloy + 5gloy2 = 15glo + 5gloy + 20glo Reorder the terms: 80glo + 25gloy + 5gloy2 = 15glo + 20glo + 5gloy Combine like terms: 15glo + 20glo = 35glo 80glo + 25gloy + 5gloy2 = 35glo + 5gloy Solving 80glo + 25gloy + 5gloy2 = 35glo + 5gloy Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-35glo' to each side of the equation. 80glo + 25gloy + -35glo + 5gloy2 = 35glo + -35glo + 5gloy Reorder the terms: 80glo + -35glo + 25gloy + 5gloy2 = 35glo + -35glo + 5gloy Combine like terms: 80glo + -35glo = 45glo 45glo + 25gloy + 5gloy2 = 35glo + -35glo + 5gloy Combine like terms: 35glo + -35glo = 0 45glo + 25gloy + 5gloy2 = 0 + 5gloy 45glo + 25gloy + 5gloy2 = 5gloy Add '-5gloy' to each side of the equation. 45glo + 25gloy + -5gloy + 5gloy2 = 5gloy + -5gloy Combine like terms: 25gloy + -5gloy = 20gloy 45glo + 20gloy + 5gloy2 = 5gloy + -5gloy Combine like terms: 5gloy + -5gloy = 0 45glo + 20gloy + 5gloy2 = 0 Factor out the Greatest Common Factor (GCF), '5glo'. 5glo(9 + 4y + y2) = 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 + 4y + y2)' equal to zero and attempt to solve: Simplifying 9 + 4y + y2 = 0 Solving 9 + 4y + y2 = 0 Move all terms containing g to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + 4y + -9 + y2 = 0 + -9 Reorder the terms: 9 + -9 + 4y + y2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 4y + y2 = 0 + -9 4y + y2 = 0 + -9 Combine like terms: 0 + -9 = -9 4y + y2 = -9 Add '-4y' to each side of the equation. 4y + -4y + y2 = -9 + -4y Combine like terms: 4y + -4y = 0 0 + y2 = -9 + -4y y2 = -9 + -4y Add '-1y2' to each side of the equation. y2 + -1y2 = -9 + -4y + -1y2 Combine like terms: y2 + -1y2 = 0 0 = -9 + -4y + -1y2 Simplifying 0 = -9 + -4y + -1y2 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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