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Simplifying Log[5](3x + 2) + -1log[5](t) = log[5](4) Reorder the terms: goL * 5(2 + 3x) + -1log[5](t) = log[5](4) Reorder the terms for easier multiplication: 5goL(2 + 3x) + -1log[5](t) = log[5](4) (2 * 5goL + 3x * 5goL) + -1log[5](t) = log[5](4) (10goL + 15goxL) + -1log[5](t) = log[5](4) Reorder the terms for easier multiplication: 10goL + 15goxL + -1 * 5glo * t = log[5](4) Multiply -1 * 5 10goL + 15goxL + -5glo * t = log[5](4) Multiply glo * t 10goL + 15goxL + -5glot = log[5](4) Reorder the terms: -5glot + 10goL + 15goxL = log[5](4) Reorder the terms for easier multiplication: -5glot + 10goL + 15goxL = 5 * 4glo Multiply 5 * 4 -5glot + 10goL + 15goxL = 20glo Solving -5glot + 10goL + 15goxL = 20glo 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. -5glot + 10goL + -20glo + 15goxL = 20glo + -20glo Reorder the terms: -20glo + -5glot + 10goL + 15goxL = 20glo + -20glo Combine like terms: 20glo + -20glo = 0 -20glo + -5glot + 10goL + 15goxL = 0 Factor out the Greatest Common Factor (GCF), '5go'. 5go(-4l + -1lt + 2L + 3xL) = 0 Ignore the factor 5.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 '(-4l + -1lt + 2L + 3xL)' equal to zero and attempt to solve: Simplifying -4l + -1lt + 2L + 3xL = 0 Reorder the terms: 2L + -4l + -1lt + 3xL = 0 Solving 2L + -4l + -1lt + 3xL = 0 Move all terms containing g to the left, all other terms to the right. Add '-2L' to each side of the equation. 2L + -4l + -1lt + -2L + 3xL = 0 + -2L Reorder the terms: 2L + -2L + -4l + -1lt + 3xL = 0 + -2L Combine like terms: 2L + -2L = 0 0 + -4l + -1lt + 3xL = 0 + -2L -4l + -1lt + 3xL = 0 + -2L Remove the zero: -4l + -1lt + 3xL = -2L Add '4l' to each side of the equation. -4l + -1lt + 4l + 3xL = -2L + 4l Reorder the terms: -4l + 4l + -1lt + 3xL = -2L + 4l Combine like terms: -4l + 4l = 0 0 + -1lt + 3xL = -2L + 4l -1lt + 3xL = -2L + 4l Add 'lt' to each side of the equation. -1lt + lt + 3xL = -2L + 4l + lt Combine like terms: -1lt + lt = 0 0 + 3xL = -2L + 4l + lt 3xL = -2L + 4l + lt Add '-3xL' to each side of the equation. 3xL + -3xL = -2L + 4l + lt + -3xL Combine like terms: 3xL + -3xL = 0 0 = -2L + 4l + lt + -3xL Simplifying 0 = -2L + 4l + lt + -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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