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Simplifying log(6)(x + 4) + -1log(6)(x) = log(6)(x + 5) Reorder the terms: glo * 6(4 + x) + -1log(6)(x) = log(6)(x + 5) Reorder the terms for easier multiplication: 6glo(4 + x) + -1log(6)(x) = log(6)(x + 5) (4 * 6glo + x * 6glo) + -1log(6)(x) = log(6)(x + 5) (24glo + 6glox) + -1log(6)(x) = log(6)(x + 5) Reorder the terms for easier multiplication: 24glo + 6glox + -1 * 6glo * x = log(6)(x + 5) Multiply -1 * 6 24glo + 6glox + -6glo * x = log(6)(x + 5) Multiply glo * x 24glo + 6glox + -6glox = log(6)(x + 5) Combine like terms: 6glox + -6glox = 0 24glo + 0 = log(6)(x + 5) 24glo = log(6)(x + 5) Reorder the terms: 24glo = glo * 6(5 + x) Reorder the terms for easier multiplication: 24glo = 6glo(5 + x) 24glo = (5 * 6glo + x * 6glo) 24glo = (30glo + 6glox) Solving 24glo = 30glo + 6glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-30glo' to each side of the equation. 24glo + -30glo = 30glo + -30glo + 6glox Combine like terms: 24glo + -30glo = -6glo -6glo = 30glo + -30glo + 6glox Combine like terms: 30glo + -30glo = 0 -6glo = 0 + 6glox -6glo = 6glox Add '-6glox' to each side of the equation. -6glo + -6glox = 6glox + -6glox Combine like terms: 6glox + -6glox = 0 -6glo + -6glox = 0 Factor out the Greatest Common Factor (GCF), '-6glo'. -6glo(1 + 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 '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 0 Move all terms containing g to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Add '-1x' to each side of the equation. x + -1x = -1 + -1x Combine like terms: x + -1x = 0 0 = -1 + -1x Simplifying 0 = -1 + -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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