10^{2x^2-10x+1}=e

解答

1 0^{2 x^{2} - 10 x + 1} = e

x = \frac{10 ln ( 10 ) + 92 ln ^{2} ( 10 ) + 8 ln ( 10 )}{4 ln ( 10 )}, x = \frac{10 ln ( 10 ) - 92 ln ^{2} ( 10 ) + 8 ln ( 10 )}{4 ln ( 10 )}

十进制

x = 4.94277 \dots, x = 0.05722 \dots

求解步骤

1 0^{2 x^{2} - 10 x + 1} = e

使用指数运算法则

(2 x^{2} - 10 x + 1) ln (10) = ln (e)

解

(2 x^{2} - 10 x + 1) ln (10) = ln (e) : x = \frac{10 ln ( 10 ) + 92 ln ^{2} ( 10 ) + 8 ln ( 10 )}{4 ln ( 10 )}, x = \frac{10 ln ( 10 ) - 92 ln ^{2} ( 10 ) + 8 ln ( 10 )}{4 ln ( 10 )}

x = \frac{10 ln ( 10 ) + 92 ln ^{2} ( 10 ) + 8 ln ( 10 )}{4 ln ( 10 )}, x = \frac{10 ln ( 10 ) - 92 ln ^{2} ( 10 ) + 8 ln ( 10 )}{4 ln ( 10 )}

2^{5^{x - 3}} = 2^{2 5^{x}}

e^{2 x} - 4 \cdot e^{x} + 4 = 0

4^{x^{2}} - 2^{x^{2}} = 240

so l v e f or x, x y = e^{x + y}

a^{x + 3} = a^{8}