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受欢迎的代数 >

5^{2m+2}-10(5^m)=3

解答

5^{2 m + 2} - 10 (5^{m}) = 3

解答

m = \frac{ln ( \frac{3}{5} )}{ln ( 5 )}

+1

十进制

m = - 0.31739 \dots

求解步骤

5^{2 m + 2} - 10 (5^{m}) = 3

使用指数运算法则

(5^{m})^{2} \cdot 5^{2} - 10 \cdot 5^{m} = 3

用

5^{m} = u

改写方程式

(u)^{2} \cdot 5^{2} - 10 u = 3

解

u^{2} \cdot 5^{2} - 10 u = 3 : u = \frac{3}{5}, u = - \frac{1}{5}

u = \frac{3}{5}, u = - \frac{1}{5}

代回

u = 5^{m}

，求解

m

解

5^{m} = \frac{3}{5} : m = \frac{ln ( \frac{3}{5} )}{ln ( 5 )}

解

5^{m} = - \frac{1}{5} : m \in R

无解

m = \frac{ln ( \frac{3}{5} )}{ln ( 5 )}

作图

流行的例子

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4 + 21 \cdot (e^{- 2027 \cdot x}) = 8

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(2^x+1)/(2^x-1)=-6

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