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Simplifying 2log[5](x) = log[5](x + 15) + log[5](4) Reorder the terms for easier multiplication: 2 * 5glo * x = log[5](x + 15) + log[5](4) Multiply 2 * 5 10glo * x = log[5](x + 15) + log[5](4) Multiply glo * x 10glox = log[5](x + 15) + log[5](4) Reorder the terms: 10glox = glo * 5(15 + x) + log[5](4) Reorder the terms for easier multiplication: 10glox = 5glo(15 + x) + log[5](4) 10glox = (15 * 5glo + x * 5glo) + log[5](4) 10glox = (75glo + 5glox) + log[5](4) Reorder the terms for easier multiplication: 10glox = 75glo + 5glox + 5 * 4glo Multiply 5 * 4 10glox = 75glo + 5glox + 20glo Reorder the terms: 10glox = 75glo + 20glo + 5glox Combine like terms: 75glo + 20glo = 95glo 10glox = 95glo + 5glox Solving 10glox = 95glo + 5glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-95glo' to each side of the equation. -95glo + 10glox = 95glo + -95glo + 5glox Combine like terms: 95glo + -95glo = 0 -95glo + 10glox = 0 + 5glox -95glo + 10glox = 5glox Add '-5glox' to each side of the equation. -95glo + 10glox + -5glox = 5glox + -5glox Combine like terms: 10glox + -5glox = 5glox -95glo + 5glox = 5glox + -5glox Combine like terms: 5glox + -5glox = 0 -95glo + 5glox = 0 Factor out the Greatest Common Factor (GCF), '5glo'. 5glo(-19 + x) = 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 '(-19 + x)' equal to zero and attempt to solve: Simplifying -19 + x = 0 Solving -19 + x = 0 Move all terms containing g to the left, all other terms to the right. Add '19' to each side of the equation. -19 + 19 + x = 0 + 19 Combine like terms: -19 + 19 = 0 0 + x = 0 + 19 x = 0 + 19 Combine like terms: 0 + 19 = 19 x = 19 Add '-1x' to each side of the equation. x + -1x = 19 + -1x Combine like terms: x + -1x = 0 0 = 19 + -1x Simplifying 0 = 19 + -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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