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Simplifying log(8)(x + 4) + log(8)(x + 2) = log(8)(8) Reorder the terms: glo * 8(4 + x) + log(8)(x + 2) = log(8)(8) Reorder the terms for easier multiplication: 8glo(4 + x) + log(8)(x + 2) = log(8)(8) (4 * 8glo + x * 8glo) + log(8)(x + 2) = log(8)(8) (32glo + 8glox) + log(8)(x + 2) = log(8)(8) Reorder the terms: 32glo + 8glox + glo * 8(2 + x) = log(8)(8) Reorder the terms for easier multiplication: 32glo + 8glox + 8glo(2 + x) = log(8)(8) 32glo + 8glox + (2 * 8glo + x * 8glo) = log(8)(8) 32glo + 8glox + (16glo + 8glox) = log(8)(8) Reorder the terms: 32glo + 16glo + 8glox + 8glox = log(8)(8) Combine like terms: 32glo + 16glo = 48glo 48glo + 8glox + 8glox = log(8)(8) Combine like terms: 8glox + 8glox = 16glox 48glo + 16glox = log(8)(8) Reorder the terms for easier multiplication: 48glo + 16glox = 8 * 8glo Multiply 8 * 8 48glo + 16glox = 64glo Solving 48glo + 16glox = 64glo Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-64glo' to each side of the equation. 48glo + -64glo + 16glox = 64glo + -64glo Combine like terms: 48glo + -64glo = -16glo -16glo + 16glox = 64glo + -64glo Combine like terms: 64glo + -64glo = 0 -16glo + 16glox = 0 Factor out the Greatest Common Factor (GCF), '16glo'. 16glo(-1 + x) = 0 Ignore the factor 16.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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