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受欢迎的代数 >

y/(log_{2)(y^3)}=6

解答

\frac{y}{lo g _{2} ( y ^{3} )} = 6

解答

y = - \frac{18 W _{- 1} ( - \frac{l n ( 2 )}{18} )}{ln ( 2 )}, y = - \frac{18 W _{0} ( - \frac{l n ( 2 )}{18} )}{ln ( 2 )}

+1

十进制

y = 125.48459 \dots, y = 1.04089 \dots

求解步骤

\frac{y}{lo g _{2} ( y ^{3} )} = 6

在两边乘以

lo g_{2} (y^{3})

y = 6 lo g_{2} (y^{3})

交换两边

6 lo g_{2} (y^{3}) = y

两边除以

6

lo g_{2} (y^{3}) = \frac{y}{6}

使用对数运算法则

3 lo g_{2} (y) = \frac{y}{6}

在两边乘以

6

3 lo g_{2} (y) \cdot 6 = \frac{y}{6} \cdot 6

化简

18 lo g_{2} (y) = y

两边除以

18

lo g_{2} (y) = \frac{y}{18}

若

f (x) = g (x)

，则

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

2^{l o g_{2} (y)} = 2^{\frac{y}{18}}

化简

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

y = 2^{\frac{y}{18}}

解

y = 2^{\frac{y}{18}} : y = - \frac{18 W _{- 1} ( - \frac{l n ( 2 )}{18} )}{ln ( 2 )}, y = - \frac{18 W _{0} ( - \frac{l n ( 2 )}{18} )}{ln ( 2 )}

y = - \frac{18 W _{- 1} ( - \frac{l n ( 2 )}{18} )}{ln ( 2 )}, y = - \frac{18 W _{0} ( - \frac{l n ( 2 )}{18} )}{ln ( 2 )}

验证解:

y = - \frac{18 W _{- 1} ( - \frac{l n ( 2 )}{18} )}{ln ( 2 )}

真

, y = - \frac{18 W _{0} ( - \frac{l n ( 2 )}{18} )}{ln ( 2 )}

真

解为

y = - \frac{18 W _{- 1} ( - \frac{l n ( 2 )}{18} )}{ln ( 2 )}, y = - \frac{18 W _{0} ( - \frac{l n ( 2 )}{18} )}{ln ( 2 )}

作图

流行的例子

ln (2 - x) + 2 = 0

- 1 = ln (x)

log_{e}(x)=ln(x)

lo g_{e} (x) = ln (x)

4 ln (4 x) = ln (2 x)

\frac{1}{x} = ln (x)