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Simplifying log(6)(x + 7) + -1log(6) * 4 = log(6)(2x + 1) Reorder the terms: glo * 6(7 + x) + -1log(6) * 4 = log(6)(2x + 1) Reorder the terms for easier multiplication: 6glo(7 + x) + -1log(6) * 4 = log(6)(2x + 1) (7 * 6glo + x * 6glo) + -1log(6) * 4 = log(6)(2x + 1) (42glo + 6glox) + -1log(6) * 4 = log(6)(2x + 1) Reorder the terms for easier multiplication: 42glo + 6glox + -1 * 6 * 4glo = log(6)(2x + 1) Multiply -1 * 6 42glo + 6glox + -6 * 4glo = log(6)(2x + 1) Multiply -6 * 4 42glo + 6glox + -24glo = log(6)(2x + 1) Reorder the terms: 42glo + -24glo + 6glox = log(6)(2x + 1) Combine like terms: 42glo + -24glo = 18glo 18glo + 6glox = log(6)(2x + 1) Reorder the terms: 18glo + 6glox = glo * 6(1 + 2x) Reorder the terms for easier multiplication: 18glo + 6glox = 6glo(1 + 2x) 18glo + 6glox = (1 * 6glo + 2x * 6glo) 18glo + 6glox = (6glo + 12glox) Solving 18glo + 6glox = 6glo + 12glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-6glo' to each side of the equation. 18glo + -6glo + 6glox = 6glo + -6glo + 12glox Combine like terms: 18glo + -6glo = 12glo 12glo + 6glox = 6glo + -6glo + 12glox Combine like terms: 6glo + -6glo = 0 12glo + 6glox = 0 + 12glox 12glo + 6glox = 12glox Add '-12glox' to each side of the equation. 12glo + 6glox + -12glox = 12glox + -12glox Combine like terms: 6glox + -12glox = -6glox 12glo + -6glox = 12glox + -12glox Combine like terms: 12glox + -12glox = 0 12glo + -6glox = 0 Factor out the Greatest Common Factor (GCF), '6glo'. 6glo(2 + -1x) = 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 '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing g to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Add 'x' to each side of the equation. -1x + x = -2 + x Combine like terms: -1x + x = 0 0 = -2 + x Simplifying 0 = -2 + x 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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