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受欢迎的代数 >

n-8log_{2}(n)=0

解答

n - 8 lo g_{2} (n) = 0

解答

n = - \frac{8 W _{- 1} ( - \frac{l n ( 2 )}{8} )}{ln ( 2 )}, n = - \frac{8 W _{0} ( - \frac{l n ( 2 )}{8} )}{ln ( 2 )}

+1

十进制

n = 43.55926 \dots, n = 1.09999 \dots

求解步骤

n - 8 lo g_{2} (n) = 0

将

n

到右边

- 8 lo g_{2} (n) = - n

两边除以

- 8

lo g_{2} (n) = \frac{n}{8}

若

f (x) = g (x)

，则

a^{f (x)} = a^{g (x)}

2^{l o g_{2} (n)} = 2^{\frac{n}{8}}

化简

2^{l o g_{2} (n)} : n

n = 2^{\frac{n}{8}}

解

n = 2^{\frac{n}{8}} : n = - \frac{8 W _{- 1} ( - \frac{l n ( 2 )}{8} )}{ln ( 2 )}, n = - \frac{8 W _{0} ( - \frac{l n ( 2 )}{8} )}{ln ( 2 )}

n = - \frac{8 W _{- 1} ( - \frac{l n ( 2 )}{8} )}{ln ( 2 )}, n = - \frac{8 W _{0} ( - \frac{l n ( 2 )}{8} )}{ln ( 2 )}

验证解:

n = - \frac{8 W _{- 1} ( - \frac{l n ( 2 )}{8} )}{ln ( 2 )}

真

, n = - \frac{8 W _{0} ( - \frac{l n ( 2 )}{8} )}{ln ( 2 )}

真

解为

n = - \frac{8 W _{- 1} ( - \frac{l n ( 2 )}{8} )}{ln ( 2 )}, n = - \frac{8 W _{0} ( - \frac{l n ( 2 )}{8} )}{ln ( 2 )}

作图

流行的例子

log_{2}(72x)-log_{2}(x+96)=3

lo g_{2} (72 x) - lo g_{2} (x + 96) = 3

lo g_{4} (y) = 1

ln(x)+ln(2x)=ln(450)

ln (x) + ln (2 x) = ln (450)

-4log_{2}(5x)=12

- 4 lo g_{2} (5 x) = 12

4log_{4}(x)=log_{2}(x+5)+4

4 lo g_{4} (x) = lo g_{2} (x + 5) + 4