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Simplifying Log(x + 4) + log(4x + 3) = 2log(2x) Reorder the terms: goL(4 + x) + log(4x + 3) = 2log(2x) (4 * goL + x * goL) + log(4x + 3) = 2log(2x) (4goL + goxL) + log(4x + 3) = 2log(2x) Reorder the terms: 4goL + goxL + glo(3 + 4x) = 2log(2x) 4goL + goxL + (3 * glo + 4x * glo) = 2log(2x) 4goL + goxL + (3glo + 4glox) = 2log(2x) Reorder the terms: 3glo + 4glox + 4goL + goxL = 2log(2x) Remove parenthesis around (2x) 3glo + 4glox + 4goL + goxL = 2glo * 2x Reorder the terms for easier multiplication: 3glo + 4glox + 4goL + goxL = 2 * 2glo * x Multiply 2 * 2 3glo + 4glox + 4goL + goxL = 4glo * x Multiply glo * x 3glo + 4glox + 4goL + goxL = 4glox Add '-4glox' to each side of the equation. 3glo + 4glox + 4goL + -4glox + goxL = 4glox + -4glox Reorder the terms: 3glo + 4glox + -4glox + 4goL + goxL = 4glox + -4glox Combine like terms: 4glox + -4glox = 0 3glo + 0 + 4goL + goxL = 4glox + -4glox 3glo + 4goL + goxL = 4glox + -4glox Combine like terms: 4glox + -4glox = 0 3glo + 4goL + goxL = 0 Solving 3glo + 4goL + goxL = 0 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Factor out the Greatest Common Factor (GCF), 'go'. go(3l + 4L + xL) = 0Subproblem 1
Set the factor 'go' equal to zero and attempt to solve: Simplifying go = 0 Solving go = 0 Move all terms containing g to the left, all other terms to the right. Simplifying go = 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 '(3l + 4L + xL)' equal to zero and attempt to solve: Simplifying 3l + 4L + xL = 0 Reorder the terms: 4L + 3l + xL = 0 Solving 4L + 3l + xL = 0 Move all terms containing g to the left, all other terms to the right. Add '-4L' to each side of the equation. 4L + 3l + -4L + xL = 0 + -4L Reorder the terms: 4L + -4L + 3l + xL = 0 + -4L Combine like terms: 4L + -4L = 0 0 + 3l + xL = 0 + -4L 3l + xL = 0 + -4L Remove the zero: 3l + xL = -4L Add '-3l' to each side of the equation. 3l + -3l + xL = -4L + -3l Combine like terms: 3l + -3l = 0 0 + xL = -4L + -3l xL = -4L + -3l Add '-1xL' to each side of the equation. xL + -1xL = -4L + -3l + -1xL Combine like terms: xL + -1xL = 0 0 = -4L + -3l + -1xL Simplifying 0 = -4L + -3l + -1xL 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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