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Simplifying log[5](x) + log[5](x + -1) = log[5](2) Reorder the terms for easier multiplication: 5glo * x + log[5](x + -1) = log[5](2) Multiply glo * x 5glox + log[5](x + -1) = log[5](2) Reorder the terms: 5glox + glo * 5(-1 + x) = log[5](2) Reorder the terms for easier multiplication: 5glox + 5glo(-1 + x) = log[5](2) 5glox + (-1 * 5glo + x * 5glo) = log[5](2) 5glox + (-5glo + 5glox) = log[5](2) Reorder the terms: -5glo + 5glox + 5glox = log[5](2) Combine like terms: 5glox + 5glox = 10glox -5glo + 10glox = log[5](2) Reorder the terms for easier multiplication: -5glo + 10glox = 5 * 2glo Multiply 5 * 2 -5glo + 10glox = 10glo Solving -5glo + 10glox = 10glo Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-10glo' to each side of the equation. -5glo + -10glo + 10glox = 10glo + -10glo Combine like terms: -5glo + -10glo = -15glo -15glo + 10glox = 10glo + -10glo Combine like terms: 10glo + -10glo = 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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