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Simplifying log(4x + -9) = log(x + 2) + log(5) Reorder the terms: glo(-9 + 4x) = log(x + 2) + log(5) (-9 * glo + 4x * glo) = log(x + 2) + log(5) (-9glo + 4glox) = log(x + 2) + log(5) Reorder the terms: -9glo + 4glox = glo(2 + x) + log(5) -9glo + 4glox = (2 * glo + x * glo) + log(5) -9glo + 4glox = (2glo + glox) + log(5) Reorder the terms for easier multiplication: -9glo + 4glox = 2glo + glox + 5glo Reorder the terms: -9glo + 4glox = 2glo + 5glo + glox Combine like terms: 2glo + 5glo = 7glo -9glo + 4glox = 7glo + glox Solving -9glo + 4glox = 7glo + glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-7glo' to each side of the equation. -9glo + -7glo + 4glox = 7glo + -7glo + glox Combine like terms: -9glo + -7glo = -16glo -16glo + 4glox = 7glo + -7glo + glox Combine like terms: 7glo + -7glo = 0 -16glo + 4glox = 0 + glox -16glo + 4glox = glox Add '-1glox' to each side of the equation. -16glo + 4glox + -1glox = glox + -1glox Combine like terms: 4glox + -1glox = 3glox -16glo + 3glox = glox + -1glox Combine like terms: glox + -1glox = 0 -16glo + 3glox = 0 Factor out the Greatest Common Factor (GCF), 'glo'. glo(-16 + 3x) = 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 '(-16 + 3x)' equal to zero and attempt to solve: Simplifying -16 + 3x = 0 Solving -16 + 3x = 0 Move all terms containing g to the left, all other terms to the right. Add '16' to each side of the equation. -16 + 16 + 3x = 0 + 16 Combine like terms: -16 + 16 = 0 0 + 3x = 0 + 16 3x = 0 + 16 Combine like terms: 0 + 16 = 16 3x = 16 Add '-3x' to each side of the equation. 3x + -3x = 16 + -3x Combine like terms: 3x + -3x = 0 0 = 16 + -3x Simplifying 0 = 16 + -3x 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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