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Simplifying log[5](3t + 2) + -1log[5] * t = log[5] * 4 Reorder the terms: glo * 5(2 + 3t) + -1log[5] * t = log[5] * 4 Reorder the terms for easier multiplication: 5glo(2 + 3t) + -1log[5] * t = log[5] * 4 (2 * 5glo + 3t * 5glo) + -1log[5] * t = log[5] * 4 (10glo + 15glot) + -1log[5] * t = log[5] * 4 Reorder the terms for easier multiplication: 10glo + 15glot + -1 * 5glo * t = log[5] * 4 Multiply -1 * 5 10glo + 15glot + -5glo * t = log[5] * 4 Multiply glo * t 10glo + 15glot + -5glot = log[5] * 4 Combine like terms: 15glot + -5glot = 10glot 10glo + 10glot = log[5] * 4 Reorder the terms for easier multiplication: 10glo + 10glot = 5 * 4glo Multiply 5 * 4 10glo + 10glot = 20glo Solving 10glo + 10glot = 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. 10glo + -20glo + 10glot = 20glo + -20glo Combine like terms: 10glo + -20glo = -10glo -10glo + 10glot = 20glo + -20glo Combine like terms: 20glo + -20glo = 0 -10glo + 10glot = 0 Factor out the Greatest Common Factor (GCF), '10glo'. 10glo(-1 + t) = 0 Ignore the factor 10.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 + t)' equal to zero and attempt to solve: Simplifying -1 + t = 0 Solving -1 + t = 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 + t = 0 + 1 Combine like terms: -1 + 1 = 0 0 + t = 0 + 1 t = 0 + 1 Combine like terms: 0 + 1 = 1 t = 1 Add '-1t' to each side of the equation. t + -1t = 1 + -1t Combine like terms: t + -1t = 0 0 = 1 + -1t Simplifying 0 = 1 + -1t 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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