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Simplifying log[5](x + 5) + -1log[5](2x + -6) = log[5] * 3 Reorder the terms: glo * 5(5 + x) + -1log[5](2x + -6) = log[5] * 3 Reorder the terms for easier multiplication: 5glo(5 + x) + -1log[5](2x + -6) = log[5] * 3 (5 * 5glo + x * 5glo) + -1log[5](2x + -6) = log[5] * 3 (25glo + 5glox) + -1log[5](2x + -6) = log[5] * 3 Reorder the terms: 25glo + 5glox + -1glo * 5(-6 + 2x) = log[5] * 3 Reorder the terms for easier multiplication: 25glo + 5glox + -1 * 5glo(-6 + 2x) = log[5] * 3 Multiply -1 * 5 25glo + 5glox + -5glo(-6 + 2x) = log[5] * 3 25glo + 5glox + (-6 * -5glo + 2x * -5glo) = log[5] * 3 25glo + 5glox + (30glo + -10glox) = log[5] * 3 Reorder the terms: 25glo + 30glo + 5glox + -10glox = log[5] * 3 Combine like terms: 25glo + 30glo = 55glo 55glo + 5glox + -10glox = log[5] * 3 Combine like terms: 5glox + -10glox = -5glox 55glo + -5glox = log[5] * 3 Reorder the terms for easier multiplication: 55glo + -5glox = 5 * 3glo Multiply 5 * 3 55glo + -5glox = 15glo Solving 55glo + -5glox = 15glo Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-15glo' to each side of the equation. 55glo + -15glo + -5glox = 15glo + -15glo Combine like terms: 55glo + -15glo = 40glo 40glo + -5glox = 15glo + -15glo Combine like terms: 15glo + -15glo = 0 40glo + -5glox = 0 Factor out the Greatest Common Factor (GCF), '5glo'. 5glo(8 + -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 '(8 + -1x)' equal to zero and attempt to solve: Simplifying 8 + -1x = 0 Solving 8 + -1x = 0 Move all terms containing g to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1x = 0 + -8 -1x = 0 + -8 Combine like terms: 0 + -8 = -8 -1x = -8 Add 'x' to each side of the equation. -1x + x = -8 + x Combine like terms: -1x + x = 0 0 = -8 + x Simplifying 0 = -8 + 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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