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受欢迎的代数 >

64n*log_{2}(n)=8n^2

解答

64 n \cdot lo g_{2} (n) = 8 n^{2}

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

64 n lo g_{2} (n) = 8 n^{2}

将

8 n^{2}

para o lado esquerdo

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

分解

64 n lo g_{2} (n) - 8 n^{2} : 8 n (8 lo g_{2} (n) - n)

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

使用零因数法则： If

ab = 0

then

a = 0

or

b = 0

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

解

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

假

, 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

solvefor x,ln(x+1)+ln(2y)=k

so l v e f or x, ln (x + 1) + ln (2 y) = k

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

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

ln (x^{2}) = 0.456

lo g_{x} (9) = - 1

solvefor r,d=ln(1+rs)

so l v e f or r, d = ln (1 + rs)