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Simplifying log(5 + 6x) = log(8x + -15) (5 * glo + 6x * glo) = log(8x + -15) (5glo + 6glox) = log(8x + -15) Reorder the terms: 5glo + 6glox = glo(-15 + 8x) 5glo + 6glox = (-15 * glo + 8x * glo) 5glo + 6glox = (-15glo + 8glox) Solving 5glo + 6glox = -15glo + 8glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '15glo' to each side of the equation. 5glo + 15glo + 6glox = -15glo + 15glo + 8glox Combine like terms: 5glo + 15glo = 20glo 20glo + 6glox = -15glo + 15glo + 8glox Combine like terms: -15glo + 15glo = 0 20glo + 6glox = 0 + 8glox 20glo + 6glox = 8glox Add '-8glox' to each side of the equation. 20glo + 6glox + -8glox = 8glox + -8glox Combine like terms: 6glox + -8glox = -2glox 20glo + -2glox = 8glox + -8glox Combine like terms: 8glox + -8glox = 0 20glo + -2glox = 0 Factor out the Greatest Common Factor (GCF), '2glo'. 2glo(10 + -1x) = 0 Ignore the factor 2.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 '(10 + -1x)' equal to zero and attempt to solve: Simplifying 10 + -1x = 0 Solving 10 + -1x = 0 Move all terms containing g to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -1x = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -1x = 0 + -10 -1x = 0 + -10 Combine like terms: 0 + -10 = -10 -1x = -10 Add 'x' to each side of the equation. -1x + x = -10 + x Combine like terms: -1x + x = 0 0 = -10 + x Simplifying 0 = -10 + x 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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