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Simplifying Log(9w + 3) = log(6w + -3) Reorder the terms: goL(3 + 9w) = log(6w + -3) (3 * goL + 9w * goL) = log(6w + -3) (3goL + 9gowL) = log(6w + -3) Reorder the terms: 3goL + 9gowL = glo(-3 + 6w) 3goL + 9gowL = (-3 * glo + 6w * glo) 3goL + 9gowL = (-3glo + 6glow) Solving 3goL + 9gowL = -3glo + 6glow Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '3glo' to each side of the equation. 3goL + 3glo + 9gowL = -3glo + 3glo + 6glow Reorder the terms: 3glo + 3goL + 9gowL = -3glo + 3glo + 6glow Combine like terms: -3glo + 3glo = 0 3glo + 3goL + 9gowL = 0 + 6glow 3glo + 3goL + 9gowL = 6glow Add '-6glow' to each side of the equation. 3glo + 3goL + -6glow + 9gowL = 6glow + -6glow Reorder the terms: 3glo + -6glow + 3goL + 9gowL = 6glow + -6glow Combine like terms: 6glow + -6glow = 0 3glo + -6glow + 3goL + 9gowL = 0 Factor out the Greatest Common Factor (GCF), '3go'. 3go(l + -2lw + L + 3wL) = 0 Ignore the factor 3.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 '(l + -2lw + L + 3wL)' equal to zero and attempt to solve: Simplifying l + -2lw + L + 3wL = 0 Reorder the terms: L + l + -2lw + 3wL = 0 Solving L + l + -2lw + 3wL = 0 Move all terms containing g to the left, all other terms to the right. Add '-1L' to each side of the equation. L + l + -2lw + -1L + 3wL = 0 + -1L Reorder the terms: L + -1L + l + -2lw + 3wL = 0 + -1L Combine like terms: L + -1L = 0 0 + l + -2lw + 3wL = 0 + -1L l + -2lw + 3wL = 0 + -1L Remove the zero: l + -2lw + 3wL = -1L Add '-1l' to each side of the equation. l + -2lw + -1l + 3wL = -1L + -1l Reorder the terms: l + -1l + -2lw + 3wL = -1L + -1l Combine like terms: l + -1l = 0 0 + -2lw + 3wL = -1L + -1l -2lw + 3wL = -1L + -1l Add '2lw' to each side of the equation. -2lw + 2lw + 3wL = -1L + -1l + 2lw Combine like terms: -2lw + 2lw = 0 0 + 3wL = -1L + -1l + 2lw 3wL = -1L + -1l + 2lw Add '-3wL' to each side of the equation. 3wL + -3wL = -1L + -1l + 2lw + -3wL Combine like terms: 3wL + -3wL = 0 0 = -1L + -1l + 2lw + -3wL Simplifying 0 = -1L + -1l + 2lw + -3wL 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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