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受欢迎的代数 >

solvefor a,f(a+2)=2^{(a+2)}

解答

求解

a, f (a + 2) = 2^{(a + 2)}

解答

a = - \frac{W ( - \frac{l n ( 2 )}{f} ) + 2 ln ( 2 )}{ln ( 2 )}

求解步骤

f (a + 2) = 2^{(a + 2)}

将

f (a + 2) = 2^{(a + 2)}

调整为朗伯形式:

f (a + 2) e^{l n (2) (- a - 2)} = 1

用

(- a - 2) ln (2) = u

和

a = - \frac{u + 2 ln ( 2 )}{ln ( 2 )}

改写方程式

f (- \frac{u + 2 ln ( 2 )}{ln ( 2 )} + 2) e^{u} = 1

改写

f ((- \frac{u + 2 ln ( 2 )}{ln ( 2 )}) + 2) e^{u} = 1

为朗伯形式:

e^{u} u = - \frac{ln ( 2 )}{f}

解

e^{u} u = - \frac{ln ( 2 )}{f} : u = W (- \frac{ln ( 2 )}{f})

u = W (- \frac{ln ( 2 )}{f})

代回

u = (- a - 2) ln (2)

，求解

a

解

(- a - 2) ln (2) = W (- \frac{ln ( 2 )}{f}) : a = - \frac{W ( - \frac{l n ( 2 )}{f} ) + 2 ln ( 2 )}{ln ( 2 )}

a = - \frac{W ( - \frac{l n ( 2 )}{f} ) + 2 ln ( 2 )}{ln ( 2 )}

作图

流行的例子

5^{x+1}+6*5^x=6

5^{x + 1} + 6 \cdot 5^{x} = 6

1.0 6^{x} = 4.1

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e^{2 x} = 1.5 (2) + x

3/4*2^{n-2}=768

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