6000(1.05)^t=5500e^{0.0495t}

解答

6000 (1.05)^{t} = 5500 e^{0.0495 t}

t = - \frac{ln ( \frac{11}{12} )}{- ln ( 1.05 ) + 0.0495}

十进制

t = 122.57957 \dots

求解步骤

6000 (1.05)^{t} = 5500 e^{0.0495 t}

使用指数运算法则

ln (6000) + t ln (1.05) = ln (5500) + 0.0495 t

解

ln (6000) + t ln (1.05) = ln (5500) + 0.0495 t : t = - \frac{ln ( \frac{11}{12} )}{- ln ( 1.05 ) + 0.0495}

t = - \frac{ln ( \frac{11}{12} )}{- ln ( 1.05 ) + 0.0495}

500 = 25 e^{2 x}

2^{x - 1} + 2^{x + 1} = 320

3^{2 x} + 5 \cdot 3^{x} = 864

1.25 = 1.3 3^{x}

e^{x} = 5.7