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Simplifying log(6)(x) + log(6)(x + 4) = log(6)(x + 18) Reorder the terms for easier multiplication: 6glo * x + log(6)(x + 4) = log(6)(x + 18) Multiply glo * x 6glox + log(6)(x + 4) = log(6)(x + 18) Reorder the terms: 6glox + glo * 6(4 + x) = log(6)(x + 18) Reorder the terms for easier multiplication: 6glox + 6glo(4 + x) = log(6)(x + 18) 6glox + (4 * 6glo + x * 6glo) = log(6)(x + 18) 6glox + (24glo + 6glox) = log(6)(x + 18) Reorder the terms: 24glo + 6glox + 6glox = log(6)(x + 18) Combine like terms: 6glox + 6glox = 12glox 24glo + 12glox = log(6)(x + 18) Reorder the terms: 24glo + 12glox = glo * 6(18 + x) Reorder the terms for easier multiplication: 24glo + 12glox = 6glo(18 + x) 24glo + 12glox = (18 * 6glo + x * 6glo) 24glo + 12glox = (108glo + 6glox) Solving 24glo + 12glox = 108glo + 6glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-108glo' to each side of the equation. 24glo + -108glo + 12glox = 108glo + -108glo + 6glox Combine like terms: 24glo + -108glo = -84glo -84glo + 12glox = 108glo + -108glo + 6glox Combine like terms: 108glo + -108glo = 0 -84glo + 12glox = 0 + 6glox -84glo + 12glox = 6glox Add '-6glox' to each side of the equation. -84glo + 12glox + -6glox = 6glox + -6glox Combine like terms: 12glox + -6glox = 6glox -84glo + 6glox = 6glox + -6glox Combine like terms: 6glox + -6glox = 0 -84glo + 6glox = 0 Factor out the Greatest Common Factor (GCF), '6glo'. 6glo(-14 + x) = 0 Ignore the factor 6.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 '(-14 + x)' equal to zero and attempt to solve: Simplifying -14 + x = 0 Solving -14 + x = 0 Move all terms containing g to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + x = 0 + 14 Combine like terms: -14 + 14 = 0 0 + x = 0 + 14 x = 0 + 14 Combine like terms: 0 + 14 = 14 x = 14 Add '-1x' to each side of the equation. x + -1x = 14 + -1x Combine like terms: x + -1x = 0 0 = 14 + -1x Simplifying 0 = 14 + -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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