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受欢迎的代数 >

n/(log_{2)(n)}=8

解答

\frac{n}{lo g _{2} ( n )} = 8

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

\frac{n}{lo g _{2} ( n )} = 8

在两边乘以

lo g_{2} (n)

n = 8 lo g_{2} (n)

交换两边

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

2log_{6}(x-7)+log_{6}(9)=2

2 lo g_{6} (x - 7) + lo g_{6} (9) = 2

log_{8}(x)=0.333

lo g_{8} (x) = 0.333

2log_{3}(x)-log_{27}(x)=10

2 lo g_{3} (x) - lo g_{27} (x) = 10

log_{125}(x)=-1/3

lo g_{125} (x) = - \frac{1}{3}

solvefor y,ln(1-2y)=-2t+c

so l v e f or y, ln (1 - 2 y) = - 2 t + c