10^{(2x)/3}=15

解答

1 0^{\frac{2 x}{3}} = 15

x = \frac{3 ln ( 15 )}{2 ln ( 10 )}

十进制

x = 1.76413 \dots

求解步骤

1 0^{\frac{2 x}{3}} = 15

使用指数运算法则

\frac{2 x}{3} ln (10) = ln (15)

解

\frac{2 x}{3} ln (10) = ln (15) : x = \frac{3 ln ( 15 )}{2 ln ( 10 )}

x = \frac{3 ln ( 15 )}{2 ln ( 10 )}

3^{5 x (- 10)} = 1

so l v e f or x, 2 e^{x} + 3 e^{- 3 x} = 0

e^{2 t + 2} = 2 e^{2 - t}

0 = 2 e^{x} - e^{- 3 x}

9^{x + 1} - 3^{x} = 6534