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Simplifying log(7)(x + -2) + log(7)(x + -4) = log(7)(15) Reorder the terms: glo * 7(-2 + x) + log(7)(x + -4) = log(7)(15) Reorder the terms for easier multiplication: 7glo(-2 + x) + log(7)(x + -4) = log(7)(15) (-2 * 7glo + x * 7glo) + log(7)(x + -4) = log(7)(15) (-14glo + 7glox) + log(7)(x + -4) = log(7)(15) Reorder the terms: -14glo + 7glox + glo * 7(-4 + x) = log(7)(15) Reorder the terms for easier multiplication: -14glo + 7glox + 7glo(-4 + x) = log(7)(15) -14glo + 7glox + (-4 * 7glo + x * 7glo) = log(7)(15) -14glo + 7glox + (-28glo + 7glox) = log(7)(15) Reorder the terms: -14glo + -28glo + 7glox + 7glox = log(7)(15) Combine like terms: -14glo + -28glo = -42glo -42glo + 7glox + 7glox = log(7)(15) Combine like terms: 7glox + 7glox = 14glox -42glo + 14glox = log(7)(15) Reorder the terms for easier multiplication: -42glo + 14glox = 7 * 15glo Multiply 7 * 15 -42glo + 14glox = 105glo Solving -42glo + 14glox = 105glo Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-105glo' to each side of the equation. -42glo + -105glo + 14glox = 105glo + -105glo Combine like terms: -42glo + -105glo = -147glo -147glo + 14glox = 105glo + -105glo Combine like terms: 105glo + -105glo = 0 -147glo + 14glox = 0 Factor out the Greatest Common Factor (GCF), '7glo'. 7glo(-21 + 2x) = 0 Ignore the factor 7.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 '(-21 + 2x)' equal to zero and attempt to solve: Simplifying -21 + 2x = 0 Solving -21 + 2x = 0 Move all terms containing g to the left, all other terms to the right. Add '21' to each side of the equation. -21 + 21 + 2x = 0 + 21 Combine like terms: -21 + 21 = 0 0 + 2x = 0 + 21 2x = 0 + 21 Combine like terms: 0 + 21 = 21 2x = 21 Add '-2x' to each side of the equation. 2x + -2x = 21 + -2x Combine like terms: 2x + -2x = 0 0 = 21 + -2x Simplifying 0 = 21 + -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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