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Simplifying log(7)(8x + 20) = log(7)(x + 6) Reorder the terms: glo * 7(20 + 8x) = log(7)(x + 6) Reorder the terms for easier multiplication: 7glo(20 + 8x) = log(7)(x + 6) (20 * 7glo + 8x * 7glo) = log(7)(x + 6) (140glo + 56glox) = log(7)(x + 6) Reorder the terms: 140glo + 56glox = glo * 7(6 + x) Reorder the terms for easier multiplication: 140glo + 56glox = 7glo(6 + x) 140glo + 56glox = (6 * 7glo + x * 7glo) 140glo + 56glox = (42glo + 7glox) Solving 140glo + 56glox = 42glo + 7glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-42glo' to each side of the equation. 140glo + -42glo + 56glox = 42glo + -42glo + 7glox Combine like terms: 140glo + -42glo = 98glo 98glo + 56glox = 42glo + -42glo + 7glox Combine like terms: 42glo + -42glo = 0 98glo + 56glox = 0 + 7glox 98glo + 56glox = 7glox Add '-7glox' to each side of the equation. 98glo + 56glox + -7glox = 7glox + -7glox Combine like terms: 56glox + -7glox = 49glox 98glo + 49glox = 7glox + -7glox Combine like terms: 7glox + -7glox = 0 98glo + 49glox = 0 Factor out the Greatest Common Factor (GCF), '49glo'. 49glo(2 + x) = 0 Ignore the factor 49.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 '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 0 Move all terms containing g to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Add '-1x' to each side of the equation. x + -1x = -2 + -1x Combine like terms: x + -1x = 0 0 = -2 + -1x Simplifying 0 = -2 + -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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