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