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受欢迎的代数 >

x/(log_{2)(4x-12)}=5

解答

\frac{x}{lo g _{2} ( 4 x - 12 )} = 5

解答

x = - \frac{5 W _{- 1} ( - \frac{e ^{\frac{3 l n ( 2 )}{5}} l n ( 2 )}{20} )}{ln ( 2 )} + 3, x = - \frac{5 W _{0} ( - \frac{e ^{\frac{3 l n ( 2 )}{5}} l n ( 2 )}{20} )}{ln ( 2 )} + 3

+1

十进制

x = 35, x = 3.40056 \dots

求解步骤

\frac{x}{lo g _{2} ( 4 x - 12 )} = 5

在两边乘以

lo g_{2} (4 x - 12)

x = 5 lo g_{2} (4 x - 12)

交换两边

5 lo g_{2} (4 x - 12) = x

两边除以

5

lo g_{2} (4 x - 12) = \frac{x}{5}

若

f (x) = g (x)

，则

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

2^{l o g_{2} (4 x - 12)} = 2^{\frac{x}{5}}

化简

2^{l o g_{2} (4 x - 12)} : 4 x - 12

4 x - 12 = 2^{\frac{x}{5}}

解

4 x - 12 = 2^{\frac{x}{5}} : x = - \frac{5 W _{- 1} ( - \frac{e ^{\frac{3 l n ( 2 )}{5}} l n ( 2 )}{20} )}{ln ( 2 )} + 3, x = - \frac{5 W _{0} ( - \frac{e ^{\frac{3 l n ( 2 )}{5}} l n ( 2 )}{20} )}{ln ( 2 )} + 3

x = - \frac{5 W _{- 1} ( - \frac{e ^{\frac{3 l n ( 2 )}{5}} l n ( 2 )}{20} )}{ln ( 2 )} + 3, x = - \frac{5 W _{0} ( - \frac{e ^{\frac{3 l n ( 2 )}{5}} l n ( 2 )}{20} )}{ln ( 2 )} + 3

验证解:

x = - \frac{5 W _{- 1} ( - \frac{e ^{\frac{3 l n ( 2 )}{5}} l n ( 2 )}{20} )}{ln ( 2 )} + 3

真

, x = - \frac{5 W _{0} ( - \frac{e ^{\frac{3 l n ( 2 )}{5}} l n ( 2 )}{20} )}{ln ( 2 )} + 3

真

解为

x = - \frac{5 W _{- 1} ( - \frac{e ^{\frac{3 l n ( 2 )}{5}} l n ( 2 )}{20} )}{ln ( 2 )} + 3, x = - \frac{5 W _{0} ( - \frac{e ^{\frac{3 l n ( 2 )}{5}} l n ( 2 )}{20} )}{ln ( 2 )} + 3

作图

流行的例子

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

ln(x+2)=2+ln(x)

ln (x + 2) = 2 + ln (x)

ln(5+e^{-2}x)=3

ln (5 + e^{- 2} x) = 3

2*(log_{5}(x))^2+3=7*log_{5}(x)

2 \cdot (lo g_{5} (x))^{2} + 3 = 7 \cdot lo g_{5} (x)

ln (x + 1) = x - 2