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Simplifying log(4)(5 + -2x) + -1log(4)(1 + -1x) = log(4)(3 + -2x) Reorder the terms for easier multiplication: 4glo(5 + -2x) + -1log(4)(1 + -1x) = log(4)(3 + -2x) (5 * 4glo + -2x * 4glo) + -1log(4)(1 + -1x) = log(4)(3 + -2x) (20glo + -8glox) + -1log(4)(1 + -1x) = log(4)(3 + -2x) Reorder the terms for easier multiplication: 20glo + -8glox + -1 * 4glo(1 + -1x) = log(4)(3 + -2x) Multiply -1 * 4 20glo + -8glox + -4glo(1 + -1x) = log(4)(3 + -2x) 20glo + -8glox + (1 * -4glo + -1x * -4glo) = log(4)(3 + -2x) 20glo + -8glox + (-4glo + 4glox) = log(4)(3 + -2x) Reorder the terms: 20glo + -4glo + -8glox + 4glox = log(4)(3 + -2x) Combine like terms: 20glo + -4glo = 16glo 16glo + -8glox + 4glox = log(4)(3 + -2x) Combine like terms: -8glox + 4glox = -4glox 16glo + -4glox = log(4)(3 + -2x) Reorder the terms for easier multiplication: 16glo + -4glox = 4glo(3 + -2x) 16glo + -4glox = (3 * 4glo + -2x * 4glo) 16glo + -4glox = (12glo + -8glox) Solving 16glo + -4glox = 12glo + -8glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-12glo' to each side of the equation. 16glo + -12glo + -4glox = 12glo + -12glo + -8glox Combine like terms: 16glo + -12glo = 4glo 4glo + -4glox = 12glo + -12glo + -8glox Combine like terms: 12glo + -12glo = 0 4glo + -4glox = 0 + -8glox 4glo + -4glox = -8glox Add '8glox' to each side of the equation. 4glo + -4glox + 8glox = -8glox + 8glox Combine like terms: -4glox + 8glox = 4glox 4glo + 4glox = -8glox + 8glox Combine like terms: -8glox + 8glox = 0 4glo + 4glox = 0 Factor out the Greatest Common Factor (GCF), '4glo'. 4glo(1 + x) = 0 Ignore the factor 4.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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