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Simplifying log(4 + -5x) = log(x + 10) (4 * glo + -5x * glo) = log(x + 10) (4glo + -5glox) = log(x + 10) Reorder the terms: 4glo + -5glox = glo(10 + x) 4glo + -5glox = (10 * glo + x * glo) 4glo + -5glox = (10glo + glox) Solving 4glo + -5glox = 10glo + glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-10glo' to each side of the equation. 4glo + -10glo + -5glox = 10glo + -10glo + glox Combine like terms: 4glo + -10glo = -6glo -6glo + -5glox = 10glo + -10glo + glox Combine like terms: 10glo + -10glo = 0 -6glo + -5glox = 0 + glox -6glo + -5glox = glox Add '-1glox' to each side of the equation. -6glo + -5glox + -1glox = glox + -1glox Combine like terms: -5glox + -1glox = -6glox -6glo + -6glox = glox + -1glox Combine like terms: glox + -1glox = 0 -6glo + -6glox = 0 Factor out the Greatest Common Factor (GCF), '-6glo'. -6glo(1 + x) = 0 Ignore the factor -6.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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