20(1.07)^x=8(1.13)^x

解答

20 (1.07)^{x} = 8 (1.13)^{x}

x = - \frac{ln ( \frac{2}{5} )}{ln ( 1.13 ) - ln ( 1.07 )}

十进制

x = 16.79449 \dots

求解步骤

20 (1.07)^{x} = 8 (1.13)^{x}

使用指数运算法则

ln (20) + x ln (1.07) = ln (8) + x ln (1.13)

解

ln (20) + x ln (1.07) = ln (8) + x ln (1.13) : x = - \frac{ln ( \frac{2}{5} )}{ln ( 1.13 ) - ln ( 1.07 )}

x = - \frac{ln ( \frac{2}{5} )}{ln ( 1.13 ) - ln ( 1.07 )}

7.9 (1.3)^{1.3 x} = 352

(1 + 0.06)^{x} = 4800000

a^{x} = 3

4005 e^{(0.04 t)} = 6218.59

3 2^{2 n + 1} = 8^{4 n - 1}