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Simplifying log(8x) = log(4x + 12) Remove parenthesis around (8x) glo * 8x = log(4x + 12) Reorder the terms for easier multiplication: 8glo * x = log(4x + 12) Multiply glo * x 8glox = log(4x + 12) Reorder the terms: 8glox = glo(12 + 4x) 8glox = (12 * glo + 4x * glo) 8glox = (12glo + 4glox) Solving 8glox = 12glo + 4glox 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. -12glo + 8glox = 12glo + -12glo + 4glox Combine like terms: 12glo + -12glo = 0 -12glo + 8glox = 0 + 4glox -12glo + 8glox = 4glox Add '-4glox' to each side of the equation. -12glo + 8glox + -4glox = 4glox + -4glox Combine like terms: 8glox + -4glox = 4glox -12glo + 4glox = 4glox + -4glox Combine like terms: 4glox + -4glox = 0 -12glo + 4glox = 0 Factor out the Greatest Common Factor (GCF), '4glo'. 4glo(-3 + x) = 0 Ignore the factor 4.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 '(-3 + x)' equal to zero and attempt to solve: Simplifying -3 + x = 0 Solving -3 + x = 0 Move all terms containing g to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + x = 0 + 3 x = 0 + 3 Combine like terms: 0 + 3 = 3 x = 3 Add '-1x' to each side of the equation. x + -1x = 3 + -1x Combine like terms: x + -1x = 0 0 = 3 + -1x Simplifying 0 = 3 + -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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