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Simplifying log[5](x + 4) + log[5](x + 3) = log[5] * 20 Reorder the terms: glo * 5(4 + x) + log[5](x + 3) = log[5] * 20 Reorder the terms for easier multiplication: 5glo(4 + x) + log[5](x + 3) = log[5] * 20 (4 * 5glo + x * 5glo) + log[5](x + 3) = log[5] * 20 (20glo + 5glox) + log[5](x + 3) = log[5] * 20 Reorder the terms: 20glo + 5glox + glo * 5(3 + x) = log[5] * 20 Reorder the terms for easier multiplication: 20glo + 5glox + 5glo(3 + x) = log[5] * 20 20glo + 5glox + (3 * 5glo + x * 5glo) = log[5] * 20 20glo + 5glox + (15glo + 5glox) = log[5] * 20 Reorder the terms: 20glo + 15glo + 5glox + 5glox = log[5] * 20 Combine like terms: 20glo + 15glo = 35glo 35glo + 5glox + 5glox = log[5] * 20 Combine like terms: 5glox + 5glox = 10glox 35glo + 10glox = log[5] * 20 Reorder the terms for easier multiplication: 35glo + 10glox = 5 * 20glo Multiply 5 * 20 35glo + 10glox = 100glo Solving 35glo + 10glox = 100glo Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-100glo' to each side of the equation. 35glo + -100glo + 10glox = 100glo + -100glo Combine like terms: 35glo + -100glo = -65glo -65glo + 10glox = 100glo + -100glo Combine like terms: 100glo + -100glo = 0 -65glo + 10glox = 0 Factor out the Greatest Common Factor (GCF), '5glo'. 5glo(-13 + 2x) = 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 '(-13 + 2x)' equal to zero and attempt to solve: Simplifying -13 + 2x = 0 Solving -13 + 2x = 0 Move all terms containing g to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + 2x = 0 + 13 Combine like terms: -13 + 13 = 0 0 + 2x = 0 + 13 2x = 0 + 13 Combine like terms: 0 + 13 = 13 2x = 13 Add '-2x' to each side of the equation. 2x + -2x = 13 + -2x Combine like terms: 2x + -2x = 0 0 = 13 + -2x Simplifying 0 = 13 + -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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