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Simplifying Log[3](t + 36) + -1log[3](t + 6) = log[3] * t Reorder the terms: goL * 3(36 + t) + -1log[3](t + 6) = log[3] * t Reorder the terms for easier multiplication: 3goL(36 + t) + -1log[3](t + 6) = log[3] * t (36 * 3goL + t * 3goL) + -1log[3](t + 6) = log[3] * t (108goL + 3gotL) + -1log[3](t + 6) = log[3] * t Reorder the terms: 108goL + 3gotL + -1glo * 3(6 + t) = log[3] * t Reorder the terms for easier multiplication: 108goL + 3gotL + -1 * 3glo(6 + t) = log[3] * t Multiply -1 * 3 108goL + 3gotL + -3glo(6 + t) = log[3] * t 108goL + 3gotL + (6 * -3glo + t * -3glo) = log[3] * t 108goL + 3gotL + (-18glo + -3glot) = log[3] * t Reorder the terms: -18glo + -3glot + 108goL + 3gotL = log[3] * t Reorder the terms for easier multiplication: -18glo + -3glot + 108goL + 3gotL = 3glo * t Multiply glo * t -18glo + -3glot + 108goL + 3gotL = 3glot Solving -18glo + -3glot + 108goL + 3gotL = 3glot Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-3glot' to each side of the equation. -18glo + -3glot + 108goL + -3glot + 3gotL = 3glot + -3glot Reorder the terms: -18glo + -3glot + -3glot + 108goL + 3gotL = 3glot + -3glot Combine like terms: -3glot + -3glot = -6glot -18glo + -6glot + 108goL + 3gotL = 3glot + -3glot Combine like terms: 3glot + -3glot = 0 -18glo + -6glot + 108goL + 3gotL = 0 Factor out the Greatest Common Factor (GCF), '3go'. 3go(-6l + -2lt + 36L + tL) = 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 '(-6l + -2lt + 36L + tL)' equal to zero and attempt to solve: Simplifying -6l + -2lt + 36L + tL = 0 Reorder the terms: 36L + -6l + -2lt + tL = 0 Solving 36L + -6l + -2lt + tL = 0 Move all terms containing g to the left, all other terms to the right. Add '-36L' to each side of the equation. 36L + -6l + -2lt + -36L + tL = 0 + -36L Reorder the terms: 36L + -36L + -6l + -2lt + tL = 0 + -36L Combine like terms: 36L + -36L = 0 0 + -6l + -2lt + tL = 0 + -36L -6l + -2lt + tL = 0 + -36L Remove the zero: -6l + -2lt + tL = -36L Add '6l' to each side of the equation. -6l + -2lt + 6l + tL = -36L + 6l Reorder the terms: -6l + 6l + -2lt + tL = -36L + 6l Combine like terms: -6l + 6l = 0 0 + -2lt + tL = -36L + 6l -2lt + tL = -36L + 6l Add '2lt' to each side of the equation. -2lt + 2lt + tL = -36L + 6l + 2lt Combine like terms: -2lt + 2lt = 0 0 + tL = -36L + 6l + 2lt tL = -36L + 6l + 2lt Add '-1tL' to each side of the equation. tL + -1tL = -36L + 6l + 2lt + -1tL Combine like terms: tL + -1tL = 0 0 = -36L + 6l + 2lt + -1tL Simplifying 0 = -36L + 6l + 2lt + -1tL 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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