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Simplifying 2 + log(5)(x + -2) = log(5)(15x) Reorder the terms: 2 + glo * 5(-2 + x) = log(5)(15x) Reorder the terms for easier multiplication: 2 + 5glo(-2 + x) = log(5)(15x) 2 + (-2 * 5glo + x * 5glo) = log(5)(15x) 2 + (-10glo + 5glox) = log(5)(15x) Remove parenthesis around (15x) 2 + -10glo + 5glox = glo * 5 * 15x Reorder the terms for easier multiplication: 2 + -10glo + 5glox = 5 * 15glo * x Multiply 5 * 15 2 + -10glo + 5glox = 75glo * x Multiply glo * x 2 + -10glo + 5glox = 75glox Solving 2 + -10glo + 5glox = 75glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-75glox' to each side of the equation. 2 + -10glo + 5glox + -75glox = 75glox + -75glox Combine like terms: 5glox + -75glox = -70glox 2 + -10glo + -70glox = 75glox + -75glox Combine like terms: 75glox + -75glox = 0 2 + -10glo + -70glox = 0 Add '-2' to each side of the equation. 2 + -10glo + -2 + -70glox = 0 + -2 Reorder the terms: 2 + -2 + -10glo + -70glox = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -10glo + -70glox = 0 + -2 -10glo + -70glox = 0 + -2 Combine like terms: 0 + -2 = -2 -10glo + -70glox = -2 Reorder the terms: 2 + -10glo + -70glox = -2 + 2 Combine like terms: -2 + 2 = 0 2 + -10glo + -70glox = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(1 + -5glo + -35glox) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1 + -5glo + -35glox)' equal to zero and attempt to solve: Simplifying 1 + -5glo + -35glox = 0 Solving 1 + -5glo + -35glox = 0 Move all terms containing g to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -5glo + -1 + -35glox = 0 + -1 Reorder the terms: 1 + -1 + -5glo + -35glox = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -5glo + -35glox = 0 + -1 -5glo + -35glox = 0 + -1 Combine like terms: 0 + -1 = -1 -5glo + -35glox = -1 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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