2^{x-5}=3

解答

2^{x - 5} = 3

x = \frac{ln ( 3 )}{ln ( 2 )} + 5

十进制

x = 6.58496 \dots

求解步骤

2^{x - 5} = 3

使用指数运算法则

(x - 5) ln (2) = ln (3)

解

(x - 5) ln (2) = ln (3) : x = \frac{ln ( 3 )}{ln ( 2 )} + 5

x = \frac{ln ( 3 )}{ln ( 2 )} + 5

7 (3^{x}) = 2 (4^{5 x - 4})

7 (3^{x}) = 3 (5^{5 x - 4})

3 (4^{x}) = 5 (7^{2 x - 2})

6 (4^{x}) = 5 (3^{3 x - 5})

6 (4^{x}) = 5 (3^{2 x - 3})