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受欢迎的代数 >

8(X)^2=64Xlog_{2}(X)

解答

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

解答

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

+1

十进制

X = 43.55926 \dots, X = 1.09999 \dots

求解步骤

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

交换两边

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

将

8 X^{2}

para o lado esquerdo

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

分解

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

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

使用零因数法则： If

ab = 0

then

a = 0

or

b = 0

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

解

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

验证解:

X = 0

假

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

真

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

真

解为

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

作图

流行的例子

lo g_{2} (x + 5) = 0

lo g_{2} (x + 5) = 6

lo g_{10} (p) = - n

solvefor v,d=20log_{10}(v)

so l v e f or v, d = 20 lo g_{10} (v)

solvefor x,y=ln^2(x)

so l v e f or x, y = ln^{2} (x)