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Simplifying Log[4](x + 5) = log[4](3x + -5) Reorder the terms: goL * 4(5 + x) = log[4](3x + -5) Reorder the terms for easier multiplication: 4goL(5 + x) = log[4](3x + -5) (5 * 4goL + x * 4goL) = log[4](3x + -5) (20goL + 4goxL) = log[4](3x + -5) Reorder the terms: 20goL + 4goxL = glo * 4(-5 + 3x) Reorder the terms for easier multiplication: 20goL + 4goxL = 4glo(-5 + 3x) 20goL + 4goxL = (-5 * 4glo + 3x * 4glo) 20goL + 4goxL = (-20glo + 12glox) Solving 20goL + 4goxL = -20glo + 12glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '20glo' to each side of the equation. 20goL + 20glo + 4goxL = -20glo + 20glo + 12glox Reorder the terms: 20glo + 20goL + 4goxL = -20glo + 20glo + 12glox Combine like terms: -20glo + 20glo = 0 20glo + 20goL + 4goxL = 0 + 12glox 20glo + 20goL + 4goxL = 12glox Add '-12glox' to each side of the equation. 20glo + 20goL + -12glox + 4goxL = 12glox + -12glox Reorder the terms: 20glo + -12glox + 20goL + 4goxL = 12glox + -12glox Combine like terms: 12glox + -12glox = 0 20glo + -12glox + 20goL + 4goxL = 0 Factor out the Greatest Common Factor (GCF), '4go'. 4go(5l + -3lx + 5L + xL) = 0 Ignore the factor 4.Subproblem 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 '(5l + -3lx + 5L + xL)' equal to zero and attempt to solve: Simplifying 5l + -3lx + 5L + xL = 0 Reorder the terms: 5L + 5l + -3lx + xL = 0 Solving 5L + 5l + -3lx + xL = 0 Move all terms containing g to the left, all other terms to the right. Add '-5L' to each side of the equation. 5L + 5l + -3lx + -5L + xL = 0 + -5L Reorder the terms: 5L + -5L + 5l + -3lx + xL = 0 + -5L Combine like terms: 5L + -5L = 0 0 + 5l + -3lx + xL = 0 + -5L 5l + -3lx + xL = 0 + -5L Remove the zero: 5l + -3lx + xL = -5L Add '-5l' to each side of the equation. 5l + -3lx + -5l + xL = -5L + -5l Reorder the terms: 5l + -5l + -3lx + xL = -5L + -5l Combine like terms: 5l + -5l = 0 0 + -3lx + xL = -5L + -5l -3lx + xL = -5L + -5l Add '3lx' to each side of the equation. -3lx + 3lx + xL = -5L + -5l + 3lx Combine like terms: -3lx + 3lx = 0 0 + xL = -5L + -5l + 3lx xL = -5L + -5l + 3lx Add '-1xL' to each side of the equation. xL + -1xL = -5L + -5l + 3lx + -1xL Combine like terms: xL + -1xL = 0 0 = -5L + -5l + 3lx + -1xL Simplifying 0 = -5L + -5l + 3lx + -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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