3^{4x+4}+3^{4x}=3^5

解答

3^{4 x + 4} + 3^{4 x} = 3^{5}

x = \frac{ln ( \frac{243}{82} )}{4 ln ( 3 )}

十进制

x = 0.24720 \dots

求解步骤

3^{4 x + 4} + 3^{4 x} = 3^{5}

使用指数运算法则

4 x ln (3) = ln (\frac{243}{82})

解

4 x ln (3) = ln (\frac{243}{82}) : x = \frac{ln ( \frac{243}{82} )}{4 ln ( 3 )}

x = \frac{ln ( \frac{243}{82} )}{4 ln ( 3 )}

3^{2 x + 2} + 3^{2 x + 1} = 108

4 9^{n - 1} + 6 = 7^{2 n - 1}

(125)^{x + 4} = 5

2 = (\frac{9}{8})^{t}

4^{x} - 4^{x - 1} = 48