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Simplifying log(7)(5x + 12) = log(7)(x) + log(7)(8) Reorder the terms: glo * 7(12 + 5x) = log(7)(x) + log(7)(8) Reorder the terms for easier multiplication: 7glo(12 + 5x) = log(7)(x) + log(7)(8) (12 * 7glo + 5x * 7glo) = log(7)(x) + log(7)(8) (84glo + 35glox) = log(7)(x) + log(7)(8) Reorder the terms for easier multiplication: 84glo + 35glox = 7glo * x + log(7)(8) Multiply glo * x 84glo + 35glox = 7glox + log(7)(8) Reorder the terms for easier multiplication: 84glo + 35glox = 7glox + 7 * 8glo Multiply 7 * 8 84glo + 35glox = 7glox + 56glo Reorder the terms: 84glo + 35glox = 56glo + 7glox Solving 84glo + 35glox = 56glo + 7glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-56glo' to each side of the equation. 84glo + -56glo + 35glox = 56glo + -56glo + 7glox Combine like terms: 84glo + -56glo = 28glo 28glo + 35glox = 56glo + -56glo + 7glox Combine like terms: 56glo + -56glo = 0 28glo + 35glox = 0 + 7glox 28glo + 35glox = 7glox Add '-7glox' to each side of the equation. 28glo + 35glox + -7glox = 7glox + -7glox Combine like terms: 35glox + -7glox = 28glox 28glo + 28glox = 7glox + -7glox Combine like terms: 7glox + -7glox = 0 28glo + 28glox = 0 Factor out the Greatest Common Factor (GCF), '28glo'. 28glo(1 + x) = 0 Ignore the factor 28.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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