\( \frac{1000000}{(1+2.91\% )^{\frac{5}{3}}}+\frac{2000000}{(1+2.91\% )^{\frac{7}{3}}}+\frac{3000000}{(1+2.91\% )^{\frac{12}{3}}}=2500000+\frac{1000000}{(1+2.91\% )^{\frac{4}{3}}}+\frac{1744325.36}{(1+2.91\% )^{\frac{x}{3}}} \)

Para resolver la ecuación: \[ \frac{1\,000\,000}{(1 + 2.91\%)^{\frac{5}{3}}} + \frac{2\,000\,000}{(1 + 2.91\%)^{\frac{7}{3}}} + \frac{3\,000\,000}{(1 + 2.91\%)^{4}} = 2\,500\,000 + \frac{1\,000\,000}{(1 + 2.91\%)^{\frac{4}{3}}} + \frac{1\,744\,325.36}{(1 + 2.91\%)^{\frac{x}{3}}} \] seguimos los siguientes pasos: 1. **Simplificamos la tasa de interés:** \[ 1 + 2.91\% = 1.0291 \] 2. **Calculamos cada término de la izquierda (LHS):** \[ \frac{1\,000\,000}{1.0291^{\frac{5}{3}}} \approx 954\,370 \] \[ \frac{2\,000\,000}{1.0291^{\frac{7}{3}}} \approx 1\,869\,000 \] \[ \frac{3\,000\,000}{1.0291^{4}} \approx 2\,676\,400 \] **Total LHS:** \[ 954\,370 + 1\,869\,000 + 2\,676\,400 \approx 5\,499\,770 \] 3. **Calculamos cada término del lado derecho (RHS):** \[ 2\,500\,000 + \frac{1\,000\,000}{1.0291^{\frac{4}{3}}} \approx 2\,500\,000 + 961\,540 \approx 3\,461\,540 \] \[ \frac{1\,744\,325.36}{1.0291^{\frac{x}{3}}} \] 4. **Igualamos LHS y RHS:** \[ 5\,499\,770 = 3\,461\,540 + \frac{1\,744\,325.36}{1.0291^{\frac{x}{3}}} \] Restamos \(3\,461\,540\) de ambos lados: \[ 2\,038\,230 = \frac{1\,744\,325.36}{1.0291^{\frac{x}{3}}} \] 5. **Despejamos \(1.0291^{\frac{x}{3}}\):** \[ 1.0291^{\frac{x}{3}} = \frac{1\,744\,325.36}{2\,038\,230} \approx 0.8550 \] 6. **Aplicamos logaritmos naturales para resolver para \(x\):** \[ \ln\left(1.0291^{\frac{x}{3}}\right) = \ln(0.8550) \] \[ \frac{x}{3} \cdot \ln(1.0291) = \ln(0.8550) \] \[ x = \frac{3 \cdot \ln(0.8550)}{\ln(1.0291)} \approx \frac{3 \cdot (-0.1573)}{0.02866} \approx -16.45 \] **Conclusión:** El valor de \(x\) es aproximadamente **-16.45**.