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Simplifying log[5](x + 2) + log[5](9 + -1x) = log[5](14x) Reorder the terms: glo * 5(2 + x) + log[5](9 + -1x) = log[5](14x) Reorder the terms for easier multiplication: 5glo(2 + x) + log[5](9 + -1x) = log[5](14x) (2 * 5glo + x * 5glo) + log[5](9 + -1x) = log[5](14x) (10glo + 5glox) + log[5](9 + -1x) = log[5](14x) Reorder the terms for easier multiplication: 10glo + 5glox + 5glo(9 + -1x) = log[5](14x) 10glo + 5glox + (9 * 5glo + -1x * 5glo) = log[5](14x) 10glo + 5glox + (45glo + -5glox) = log[5](14x) Reorder the terms: 10glo + 45glo + 5glox + -5glox = log[5](14x) Combine like terms: 10glo + 45glo = 55glo 55glo + 5glox + -5glox = log[5](14x) Combine like terms: 5glox + -5glox = 0 55glo + 0 = log[5](14x) 55glo = log[5](14x) Remove parenthesis around (14x) 55glo = glo * 5 * 14x Reorder the terms for easier multiplication: 55glo = 5 * 14glo * x Multiply 5 * 14 55glo = 70glo * x Multiply glo * x 55glo = 70glox Solving 55glo = 70glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-70glox' to each side of the equation. 55glo + -70glox = 70glox + -70glox Combine like terms: 70glox + -70glox = 0 55glo + -70glox = 0 Factor out the Greatest Common Factor (GCF), '5glo'. 5glo(11 + -14x) = 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 '(11 + -14x)' equal to zero and attempt to solve: Simplifying 11 + -14x = 0 Solving 11 + -14x = 0 Move all terms containing g to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + -14x = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -14x = 0 + -11 -14x = 0 + -11 Combine like terms: 0 + -11 = -11 -14x = -11 Add '14x' to each side of the equation. -14x + 14x = -11 + 14x Combine like terms: -14x + 14x = 0 0 = -11 + 14x Simplifying 0 = -11 + 14x 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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