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