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Simplifying log(x + -3) = log(7x + -23) + -1log(x + 1) Reorder the terms: glo(-3 + x) = log(7x + -23) + -1log(x + 1) (-3 * glo + x * glo) = log(7x + -23) + -1log(x + 1) (-3glo + glox) = log(7x + -23) + -1log(x + 1) Reorder the terms: -3glo + glox = glo(-23 + 7x) + -1log(x + 1) -3glo + glox = (-23 * glo + 7x * glo) + -1log(x + 1) -3glo + glox = (-23glo + 7glox) + -1log(x + 1) Reorder the terms: -3glo + glox = -23glo + 7glox + -1glo(1 + x) -3glo + glox = -23glo + 7glox + (1 * -1glo + x * -1glo) -3glo + glox = -23glo + 7glox + (-1glo + -1glox) Reorder the terms: -3glo + glox = -23glo + -1glo + 7glox + -1glox Combine like terms: -23glo + -1glo = -24glo -3glo + glox = -24glo + 7glox + -1glox Combine like terms: 7glox + -1glox = 6glox -3glo + glox = -24glo + 6glox Solving -3glo + glox = -24glo + 6glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '24glo' to each side of the equation. -3glo + 24glo + glox = -24glo + 24glo + 6glox Combine like terms: -3glo + 24glo = 21glo 21glo + glox = -24glo + 24glo + 6glox Combine like terms: -24glo + 24glo = 0 21glo + glox = 0 + 6glox 21glo + glox = 6glox Add '-6glox' to each side of the equation. 21glo + glox + -6glox = 6glox + -6glox Combine like terms: glox + -6glox = -5glox 21glo + -5glox = 6glox + -6glox Combine like terms: 6glox + -6glox = 0 21glo + -5glox = 0 Factor out the Greatest Common Factor (GCF), 'glo'. glo(21 + -5x) = 0Subproblem 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 + -5x)' equal to zero and attempt to solve: Simplifying 21 + -5x = 0 Solving 21 + -5x = 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 + -5x = 0 + -21 Combine like terms: 21 + -21 = 0 0 + -5x = 0 + -21 -5x = 0 + -21 Combine like terms: 0 + -21 = -21 -5x = -21 Add '5x' to each side of the equation. -5x + 5x = -21 + 5x Combine like terms: -5x + 5x = 0 0 = -21 + 5x Simplifying 0 = -21 + 5x 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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