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Simplifying log(8x + -5) = log(x + 3) + log(9) Reorder the terms: glo(-5 + 8x) = log(x + 3) + log(9) (-5 * glo + 8x * glo) = log(x + 3) + log(9) (-5glo + 8glox) = log(x + 3) + log(9) Reorder the terms: -5glo + 8glox = glo(3 + x) + log(9) -5glo + 8glox = (3 * glo + x * glo) + log(9) -5glo + 8glox = (3glo + glox) + log(9) Reorder the terms for easier multiplication: -5glo + 8glox = 3glo + glox + 9glo Reorder the terms: -5glo + 8glox = 3glo + 9glo + glox Combine like terms: 3glo + 9glo = 12glo -5glo + 8glox = 12glo + glox Solving -5glo + 8glox = 12glo + glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-12glo' to each side of the equation. -5glo + -12glo + 8glox = 12glo + -12glo + glox Combine like terms: -5glo + -12glo = -17glo -17glo + 8glox = 12glo + -12glo + glox Combine like terms: 12glo + -12glo = 0 -17glo + 8glox = 0 + glox -17glo + 8glox = glox Add '-1glox' to each side of the equation. -17glo + 8glox + -1glox = glox + -1glox Combine like terms: 8glox + -1glox = 7glox -17glo + 7glox = glox + -1glox Combine like terms: glox + -1glox = 0 -17glo + 7glox = 0 Factor out the Greatest Common Factor (GCF), 'glo'. glo(-17 + 7x) = 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 '(-17 + 7x)' equal to zero and attempt to solve: Simplifying -17 + 7x = 0 Solving -17 + 7x = 0 Move all terms containing g to the left, all other terms to the right. Add '17' to each side of the equation. -17 + 17 + 7x = 0 + 17 Combine like terms: -17 + 17 = 0 0 + 7x = 0 + 17 7x = 0 + 17 Combine like terms: 0 + 17 = 17 7x = 17 Add '-7x' to each side of the equation. 7x + -7x = 17 + -7x Combine like terms: 7x + -7x = 0 0 = 17 + -7x Simplifying 0 = 17 + -7x 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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