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Simplifying 2log3x = log3(x + 6) Reorder the terms: 2g3lox = g3lo(6 + x) 2g3lox = (6 * g3lo + x * g3lo) 2g3lox = (6g3lo + g3lox) Solving 2g3lox = 6g3lo + g3lox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-6g3lo' to each side of the equation. -6g3lo + 2g3lox = 6g3lo + -6g3lo + g3lox Combine like terms: 6g3lo + -6g3lo = 0 -6g3lo + 2g3lox = 0 + g3lox -6g3lo + 2g3lox = g3lox Add '-1g3lox' to each side of the equation. -6g3lo + 2g3lox + -1g3lox = g3lox + -1g3lox Combine like terms: 2g3lox + -1g3lox = 1g3lox -6g3lo + 1g3lox = g3lox + -1g3lox Combine like terms: g3lox + -1g3lox = 0 -6g3lo + 1g3lox = 0 Factor out the Greatest Common Factor (GCF), 'g3lo'. g3lo(-6 + x) = 0Subproblem 1
Set the factor 'g3lo' equal to zero and attempt to solve: Simplifying g3lo = 0 Solving g3lo = 0 Move all terms containing g to the left, all other terms to the right. Simplifying g3lo = 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 '(-6 + x)' equal to zero and attempt to solve: Simplifying -6 + x = 0 Solving -6 + x = 0 Move all terms containing g to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 0 + 6 Combine like terms: -6 + 6 = 0 0 + x = 0 + 6 x = 0 + 6 Combine like terms: 0 + 6 = 6 x = 6 Add '-1x' to each side of the equation. x + -1x = 6 + -1x Combine like terms: x + -1x = 0 0 = 6 + -1x Simplifying 0 = 6 + -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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