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Simplifying log(7)(3x + 2) + log(7)(x) = log(7)(4) Reorder the terms: glo * 7(2 + 3x) + log(7)(x) = log(7)(4) Reorder the terms for easier multiplication: 7glo(2 + 3x) + log(7)(x) = log(7)(4) (2 * 7glo + 3x * 7glo) + log(7)(x) = log(7)(4) (14glo + 21glox) + log(7)(x) = log(7)(4) Reorder the terms for easier multiplication: 14glo + 21glox + 7glo * x = log(7)(4) Multiply glo * x 14glo + 21glox + 7glox = log(7)(4) Combine like terms: 21glox + 7glox = 28glox 14glo + 28glox = log(7)(4) Reorder the terms for easier multiplication: 14glo + 28glox = 7 * 4glo Multiply 7 * 4 14glo + 28glox = 28glo Solving 14glo + 28glox = 28glo Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-28glo' to each side of the equation. 14glo + -28glo + 28glox = 28glo + -28glo Combine like terms: 14glo + -28glo = -14glo -14glo + 28glox = 28glo + -28glo Combine like terms: 28glo + -28glo = 0 -14glo + 28glox = 0 Factor out the Greatest Common Factor (GCF), '14glo'. 14glo(-1 + 2x) = 0 Ignore the factor 14.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 + 2x)' equal to zero and attempt to solve: Simplifying -1 + 2x = 0 Solving -1 + 2x = 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 + 2x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 2x = 0 + 1 2x = 0 + 1 Combine like terms: 0 + 1 = 1 2x = 1 Add '-2x' to each side of the equation. 2x + -2x = 1 + -2x Combine like terms: 2x + -2x = 0 0 = 1 + -2x Simplifying 0 = 1 + -2x 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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