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Simplifying 2log[5](3 + -1x) + -1log[5](2) = log[5](50) Reorder the terms for easier multiplication: 2 * 5glo(3 + -1x) + -1log[5](2) = log[5](50) Multiply 2 * 5 10glo(3 + -1x) + -1log[5](2) = log[5](50) (3 * 10glo + -1x * 10glo) + -1log[5](2) = log[5](50) (30glo + -10glox) + -1log[5](2) = log[5](50) Reorder the terms for easier multiplication: 30glo + -10glox + -1 * 5 * 2glo = log[5](50) Multiply -1 * 5 30glo + -10glox + -5 * 2glo = log[5](50) Multiply -5 * 2 30glo + -10glox + -10glo = log[5](50) Reorder the terms: 30glo + -10glo + -10glox = log[5](50) Combine like terms: 30glo + -10glo = 20glo 20glo + -10glox = log[5](50) Reorder the terms for easier multiplication: 20glo + -10glox = 5 * 50glo Multiply 5 * 50 20glo + -10glox = 250glo Solving 20glo + -10glox = 250glo Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-250glo' to each side of the equation. 20glo + -250glo + -10glox = 250glo + -250glo Combine like terms: 20glo + -250glo = -230glo -230glo + -10glox = 250glo + -250glo Combine like terms: 250glo + -250glo = 0 -230glo + -10glox = 0 Factor out the Greatest Common Factor (GCF), '-10glo'. -10glo(23 + 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 '(23 + x)' equal to zero and attempt to solve: Simplifying 23 + x = 0 Solving 23 + x = 0 Move all terms containing g to the left, all other terms to the right. Add '-23' to each side of the equation. 23 + -23 + x = 0 + -23 Combine like terms: 23 + -23 = 0 0 + x = 0 + -23 x = 0 + -23 Combine like terms: 0 + -23 = -23 x = -23 Add '-1x' to each side of the equation. x + -1x = -23 + -1x Combine like terms: x + -1x = 0 0 = -23 + -1x Simplifying 0 = -23 + -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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