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Simplifying log[5](7x + 6) = 3log[5](x) Reorder the terms: glo * 5(6 + 7x) = 3log[5](x) Reorder the terms for easier multiplication: 5glo(6 + 7x) = 3log[5](x) (6 * 5glo + 7x * 5glo) = 3log[5](x) (30glo + 35glox) = 3log[5](x) Reorder the terms for easier multiplication: 30glo + 35glox = 3 * 5glo * x Multiply 3 * 5 30glo + 35glox = 15glo * x Multiply glo * x 30glo + 35glox = 15glox Solving 30glo + 35glox = 15glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-15glox' to each side of the equation. 30glo + 35glox + -15glox = 15glox + -15glox Combine like terms: 35glox + -15glox = 20glox 30glo + 20glox = 15glox + -15glox Combine like terms: 15glox + -15glox = 0 30glo + 20glox = 0 Factor out the Greatest Common Factor (GCF), '10glo'. 10glo(3 + 2x) = 0 Ignore the factor 10.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 '(3 + 2x)' equal to zero and attempt to solve: Simplifying 3 + 2x = 0 Solving 3 + 2x = 0 Move all terms containing g to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + 2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2x = 0 + -3 2x = 0 + -3 Combine like terms: 0 + -3 = -3 2x = -3 Add '-2x' to each side of the equation. 2x + -2x = -3 + -2x Combine like terms: 2x + -2x = 0 0 = -3 + -2x Simplifying 0 = -3 + -2x 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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