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Simplifying 2log[5](x + -3) + -1log[5](8) = log[5](2) Reorder the terms: 2glo * 5(-3 + x) + -1log[5](8) = log[5](2) Reorder the terms for easier multiplication: 2 * 5glo(-3 + x) + -1log[5](8) = log[5](2) Multiply 2 * 5 10glo(-3 + x) + -1log[5](8) = log[5](2) (-3 * 10glo + x * 10glo) + -1log[5](8) = log[5](2) (-30glo + 10glox) + -1log[5](8) = log[5](2) Reorder the terms for easier multiplication: -30glo + 10glox + -1 * 5 * 8glo = log[5](2) Multiply -1 * 5 -30glo + 10glox + -5 * 8glo = log[5](2) Multiply -5 * 8 -30glo + 10glox + -40glo = log[5](2) Reorder the terms: -30glo + -40glo + 10glox = log[5](2) Combine like terms: -30glo + -40glo = -70glo -70glo + 10glox = log[5](2) Reorder the terms for easier multiplication: -70glo + 10glox = 5 * 2glo Multiply 5 * 2 -70glo + 10glox = 10glo Solving -70glo + 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. -70glo + -10glo + 10glox = 10glo + -10glo Combine like terms: -70glo + -10glo = -80glo -80glo + 10glox = 10glo + -10glo Combine like terms: 10glo + -10glo = 0 -80glo + 10glox = 0 Factor out the Greatest Common Factor (GCF), '10glo'. 10glo(-8 + x) = 0 Ignore the factor 10.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 + x)' equal to zero and attempt to solve: Simplifying -8 + x = 0 Solving -8 + x = 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 + x = 0 + 8 Combine like terms: -8 + 8 = 0 0 + x = 0 + 8 x = 0 + 8 Combine like terms: 0 + 8 = 8 x = 8 Add '-1x' to each side of the equation. x + -1x = 8 + -1x Combine like terms: x + -1x = 0 0 = 8 + -1x Simplifying 0 = 8 + -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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