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Simplifying Log(8)(4 + -3x) = log(8)(5x + -3) Reorder the terms for easier multiplication: 8goL(4 + -3x) = log(8)(5x + -3) (4 * 8goL + -3x * 8goL) = log(8)(5x + -3) (32goL + -24goxL) = log(8)(5x + -3) Reorder the terms: 32goL + -24goxL = glo * 8(-3 + 5x) Reorder the terms for easier multiplication: 32goL + -24goxL = 8glo(-3 + 5x) 32goL + -24goxL = (-3 * 8glo + 5x * 8glo) 32goL + -24goxL = (-24glo + 40glox) Solving 32goL + -24goxL = -24glo + 40glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '24glo' to each side of the equation. 32goL + 24glo + -24goxL = -24glo + 24glo + 40glox Reorder the terms: 24glo + 32goL + -24goxL = -24glo + 24glo + 40glox Combine like terms: -24glo + 24glo = 0 24glo + 32goL + -24goxL = 0 + 40glox 24glo + 32goL + -24goxL = 40glox Add '-40glox' to each side of the equation. 24glo + 32goL + -40glox + -24goxL = 40glox + -40glox Reorder the terms: 24glo + -40glox + 32goL + -24goxL = 40glox + -40glox Combine like terms: 40glox + -40glox = 0 24glo + -40glox + 32goL + -24goxL = 0 Factor out the Greatest Common Factor (GCF), '8go'. 8go(3l + -5lx + 4L + -3xL) = 0 Ignore the factor 8.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 '(3l + -5lx + 4L + -3xL)' equal to zero and attempt to solve: Simplifying 3l + -5lx + 4L + -3xL = 0 Reorder the terms: 4L + 3l + -5lx + -3xL = 0 Solving 4L + 3l + -5lx + -3xL = 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 + -5lx + -4L + -3xL = 0 + -4L Reorder the terms: 4L + -4L + 3l + -5lx + -3xL = 0 + -4L Combine like terms: 4L + -4L = 0 0 + 3l + -5lx + -3xL = 0 + -4L 3l + -5lx + -3xL = 0 + -4L Remove the zero: 3l + -5lx + -3xL = -4L Add '-3l' to each side of the equation. 3l + -5lx + -3l + -3xL = -4L + -3l Reorder the terms: 3l + -3l + -5lx + -3xL = -4L + -3l Combine like terms: 3l + -3l = 0 0 + -5lx + -3xL = -4L + -3l -5lx + -3xL = -4L + -3l Add '5lx' to each side of the equation. -5lx + 5lx + -3xL = -4L + -3l + 5lx Combine like terms: -5lx + 5lx = 0 0 + -3xL = -4L + -3l + 5lx -3xL = -4L + -3l + 5lx Add '3xL' to each side of the equation. -3xL + 3xL = -4L + -3l + 5lx + 3xL Combine like terms: -3xL + 3xL = 0 0 = -4L + -3l + 5lx + 3xL Simplifying 0 = -4L + -3l + 5lx + 3xL 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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