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Simplifying log[3](7t + 5) + -1log[3] * t = log[3] * 8 Reorder the terms: glo * 3(5 + 7t) + -1log[3] * t = log[3] * 8 Reorder the terms for easier multiplication: 3glo(5 + 7t) + -1log[3] * t = log[3] * 8 (5 * 3glo + 7t * 3glo) + -1log[3] * t = log[3] * 8 (15glo + 21glot) + -1log[3] * t = log[3] * 8 Reorder the terms for easier multiplication: 15glo + 21glot + -1 * 3glo * t = log[3] * 8 Multiply -1 * 3 15glo + 21glot + -3glo * t = log[3] * 8 Multiply glo * t 15glo + 21glot + -3glot = log[3] * 8 Combine like terms: 21glot + -3glot = 18glot 15glo + 18glot = log[3] * 8 Reorder the terms for easier multiplication: 15glo + 18glot = 3 * 8glo Multiply 3 * 8 15glo + 18glot = 24glo Solving 15glo + 18glot = 24glo 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. 15glo + -24glo + 18glot = 24glo + -24glo Combine like terms: 15glo + -24glo = -9glo -9glo + 18glot = 24glo + -24glo Combine like terms: 24glo + -24glo = 0 -9glo + 18glot = 0 Factor out the Greatest Common Factor (GCF), '9glo'. 9glo(-1 + 2t) = 0 Ignore the factor 9.Subproblem 1
Set the factor 'glo' equal to zero and attempt to solve: Simplifying glo = 0 Solving glo = 0 Move all terms containing g to the left, all other terms to the right. Simplifying glo = 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 '(-1 + 2t)' equal to zero and attempt to solve: Simplifying -1 + 2t = 0 Solving -1 + 2t = 0 Move all terms containing g to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + 2t = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 2t = 0 + 1 2t = 0 + 1 Combine like terms: 0 + 1 = 1 2t = 1 Add '-2t' to each side of the equation. 2t + -2t = 1 + -2t Combine like terms: 2t + -2t = 0 0 = 1 + -2t Simplifying 0 = 1 + -2t 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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