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Simplifying log[5](5x) + -1log[5](x + -2) = log[5](x + 6) + -1log[5](x) Remove parenthesis around (5x) glo * 5 * 5x + -1log[5](x + -2) = log[5](x + 6) + -1log[5](x) Reorder the terms for easier multiplication: 5 * 5glo * x + -1log[5](x + -2) = log[5](x + 6) + -1log[5](x) Multiply 5 * 5 25glo * x + -1log[5](x + -2) = log[5](x + 6) + -1log[5](x) Multiply glo * x 25glox + -1log[5](x + -2) = log[5](x + 6) + -1log[5](x) Reorder the terms: 25glox + -1glo * 5(-2 + x) = log[5](x + 6) + -1log[5](x) Reorder the terms for easier multiplication: 25glox + -1 * 5glo(-2 + x) = log[5](x + 6) + -1log[5](x) Multiply -1 * 5 25glox + -5glo(-2 + x) = log[5](x + 6) + -1log[5](x) 25glox + (-2 * -5glo + x * -5glo) = log[5](x + 6) + -1log[5](x) 25glox + (10glo + -5glox) = log[5](x + 6) + -1log[5](x) Reorder the terms: 10glo + 25glox + -5glox = log[5](x + 6) + -1log[5](x) Combine like terms: 25glox + -5glox = 20glox 10glo + 20glox = log[5](x + 6) + -1log[5](x) Reorder the terms: 10glo + 20glox = glo * 5(6 + x) + -1log[5](x) Reorder the terms for easier multiplication: 10glo + 20glox = 5glo(6 + x) + -1log[5](x) 10glo + 20glox = (6 * 5glo + x * 5glo) + -1log[5](x) 10glo + 20glox = (30glo + 5glox) + -1log[5](x) Reorder the terms for easier multiplication: 10glo + 20glox = 30glo + 5glox + -1 * 5glo * x Multiply -1 * 5 10glo + 20glox = 30glo + 5glox + -5glo * x Multiply glo * x 10glo + 20glox = 30glo + 5glox + -5glox Combine like terms: 5glox + -5glox = 0 10glo + 20glox = 30glo + 0 10glo + 20glox = 30glo Solving 10glo + 20glox = 30glo Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-30glo' to each side of the equation. 10glo + -30glo + 20glox = 30glo + -30glo Combine like terms: 10glo + -30glo = -20glo -20glo + 20glox = 30glo + -30glo Combine like terms: 30glo + -30glo = 0 -20glo + 20glox = 0 Factor out the Greatest Common Factor (GCF), '20glo'. 20glo(-1 + x) = 0 Ignore the factor 20.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 '(-1 + x)' equal to zero and attempt to solve: Simplifying -1 + x = 0 Solving -1 + x = 0 Move all terms containing g to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + x = 0 + 1 x = 0 + 1 Combine like terms: 0 + 1 = 1 x = 1 Add '-1x' to each side of the equation. x + -1x = 1 + -1x Combine like terms: x + -1x = 0 0 = 1 + -1x Simplifying 0 = 1 + -1x 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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