3^{2t+1}=5^{3t-1}

解答

3^{2 t + 1} = 5^{3 t - 1}

t = \frac{ln ( 15 )}{3 ln ( 5 ) - 2 ln ( 3 )}

十进制

t = 1.02925 \dots

求解步骤

3^{2 t + 1} = 5^{3 t - 1}

使用指数运算法则

(2 t + 1) ln (3) = (3 t - 1) ln (5)

解

(2 t + 1) ln (3) = (3 t - 1) ln (5) : t = \frac{ln ( 15 )}{3 ln ( 5 ) - 2 ln ( 3 )}

t = \frac{ln ( 15 )}{3 ln ( 5 ) - 2 ln ( 3 )}

1 4^{x} = 3

12.5 = 15 (1 - e^{- k (30)})

2800 = 4000 - 3000 e^{5 k}

3^{x + 4} = 6^{2 x - 5}

5 (2^{x}) = 4