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受欢迎的代数 >

log_{2}(100)=n-2log_{2}(n)

解答

lo g_{2} (100) = n - 2 lo g_{2} (n)

解答

n = - \frac{2 W _{- 1} ( - \frac{l n ( 2 )}{20} )}{ln ( 2 )}, n = - \frac{2 W _{0} ( - \frac{l n ( 2 )}{20} )}{ln ( 2 )}

+1

十进制

n = 14.32472 \dots, n = 0.10365 \dots

求解步骤

lo g_{2} (100) = n - 2 lo g_{2} (n)

交换两边

n - 2 lo g_{2} (n) = lo g_{2} (100)

将

n

到右边

- 2 lo g_{2} (n) = lo g_{2} (100) - n

两边除以

- 2

lo g_{2} (n) = - \frac{lo g _{2} ( 100 ) - n}{2}

使用对数运算法则

lo g_{2} (n) = - \frac{2 lo g _{2} ( 10 ) - n}{2}

若

f (x) = g (x)

，则

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

2^{l o g_{2} (n)} = 2^{- \frac{2 l o g _{2} ( 10 ) - n}{2}}

化简

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

n = 2^{- \frac{2 l o g _{2} ( 10 ) - n}{2}}

解

n = 2^{- \frac{2 l o g _{2} ( 10 ) - n}{2}} : n = - \frac{2 W _{- 1} ( - \frac{l n ( 2 )}{20} )}{ln ( 2 )}, n = - \frac{2 W _{0} ( - \frac{l n ( 2 )}{20} )}{ln ( 2 )}

n = - \frac{2 W _{- 1} ( - \frac{l n ( 2 )}{20} )}{ln ( 2 )}, n = - \frac{2 W _{0} ( - \frac{l n ( 2 )}{20} )}{ln ( 2 )}

验证解:

n = - \frac{2 W _{- 1} ( - \frac{l n ( 2 )}{20} )}{ln ( 2 )}

真

, n = - \frac{2 W _{0} ( - \frac{l n ( 2 )}{20} )}{ln ( 2 )}

真

解为

n = - \frac{2 W _{- 1} ( - \frac{l n ( 2 )}{20} )}{ln ( 2 )}, n = - \frac{2 W _{0} ( - \frac{l n ( 2 )}{20} )}{ln ( 2 )}

作图

流行的例子

ln(7)=ln(q^2)+5-ln(10)

ln (7) = ln (q^{2}) + 5 - ln (10)

log_{10}(x)=130

lo g_{10} (x) = 130

solvefor x,ln(y)=x+ln(x-5)+c

so l v e f or x, ln (y) = x + ln (x - 5) + c

log_{5}(1log_{3}(x))=0

lo g_{5} (1 lo g_{3} (x)) = 0

ln(x)=ln(x-1)+1

ln (x) = ln (x - 1) + 1