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Simplifying log[6](6x + 5) + -1log[6](x + -6) = 2 Reorder the terms: glo * 6(5 + 6x) + -1log[6](x + -6) = 2 Reorder the terms for easier multiplication: 6glo(5 + 6x) + -1log[6](x + -6) = 2 (5 * 6glo + 6x * 6glo) + -1log[6](x + -6) = 2 (30glo + 36glox) + -1log[6](x + -6) = 2 Reorder the terms: 30glo + 36glox + -1glo * 6(-6 + x) = 2 Reorder the terms for easier multiplication: 30glo + 36glox + -1 * 6glo(-6 + x) = 2 Multiply -1 * 6 30glo + 36glox + -6glo(-6 + x) = 2 30glo + 36glox + (-6 * -6glo + x * -6glo) = 2 30glo + 36glox + (36glo + -6glox) = 2 Reorder the terms: 30glo + 36glo + 36glox + -6glox = 2 Combine like terms: 30glo + 36glo = 66glo 66glo + 36glox + -6glox = 2 Combine like terms: 36glox + -6glox = 30glox 66glo + 30glox = 2 Solving 66glo + 30glox = 2 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Reorder the terms: -2 + 66glo + 30glox = 2 + -2 Combine like terms: 2 + -2 = 0 -2 + 66glo + 30glox = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-1 + 33glo + 15glox) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + 33glo + 15glox)' equal to zero and attempt to solve: Simplifying -1 + 33glo + 15glox = 0 Solving -1 + 33glo + 15glox = 0 Move all terms containing g to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 33glo + 1 + 15glox = 0 + 1 Reorder the terms: -1 + 1 + 33glo + 15glox = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 33glo + 15glox = 0 + 1 33glo + 15glox = 0 + 1 Combine like terms: 0 + 1 = 1 33glo + 15glox = 1 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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