7^{3x+1}=5^x

解答

7^{3 x + 1} = 5^{x}

x = - \frac{ln ( 7 )}{3 ln ( 7 ) - ln ( 5 )}

十进制

x = - 0.46021 \dots

求解步骤

7^{3 x + 1} = 5^{x}

使用指数运算法则

(3 x + 1) ln (7) = x ln (5)

解

(3 x + 1) ln (7) = x ln (5) : x = - \frac{ln ( 7 )}{3 ln ( 7 ) - ln ( 5 )}

x = - \frac{ln ( 7 )}{3 ln ( 7 ) - ln ( 5 )}

(\frac{1}{4})^{x} + (\frac{1}{2})^{x} - 6 = 0

8 \cdot 3^{n - 1} - 21 = 51

3^{2 x} - 10 \times 3^{x} + 21 = 0

9 \cdot 2^{2 x} = 1

3 \frac{2 ^{7} - 2 ^{x}}{2 ^{x} - 2} = 2