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受欢迎的代数 >

2log_{10}(x+2)=x

解答

2 lo g_{10} (x + 2) = x

解答

x = - \frac{2 W _{- 1} ( - \frac{l n ( 10 )}{20} )}{ln ( 10 )} - 2, x = - \frac{2 W _{0} ( - \frac{l n ( 10 )}{20} )}{ln ( 10 )} - 2

+1

十进制

x = 0.93530 \dots, x = - 1.88597 \dots

求解步骤

2 lo g_{10} (x + 2) = x

两边除以

2

lo g_{10} (x + 2) = \frac{x}{2}

若

f (x) = g (x)

，则

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

1 0^{l o g_{10} (x + 2)} = 1 0^{\frac{x}{2}}

化简

1 0^{l o g_{10} (x + 2)} : x + 2

x + 2 = 1 0^{\frac{x}{2}}

解

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

x = - \frac{2 W _{- 1} ( - \frac{l n ( 10 )}{20} )}{ln ( 10 )} - 2, x = - \frac{2 W _{0} ( - \frac{l n ( 10 )}{20} )}{ln ( 10 )} - 2

验证解:

x = - \frac{2 W _{- 1} ( - \frac{l n ( 10 )}{20} )}{ln ( 10 )} - 2

真

, x = - \frac{2 W _{0} ( - \frac{l n ( 10 )}{20} )}{ln ( 10 )} - 2

真

解为

x = - \frac{2 W _{- 1} ( - \frac{l n ( 10 )}{20} )}{ln ( 10 )} - 2, x = - \frac{2 W _{0} ( - \frac{l n ( 10 )}{20} )}{ln ( 10 )} - 2

作图

流行的例子

4=5log_{10}(x)-log_{2}(x)

4 = 5 lo g_{10} (x) - lo g_{2} (x)

log_{2}(x+1)=-3

lo g_{2} (x + 1) = - 3

4(log_{5}(x)+log_{x}(5))=10

4 (lo g_{5} (x) + lo g_{x} (5)) = 10

solvefor x,y-1=ln(x)

so l v e f or x, y - 1 = ln (x)

ln(x)+ln(x^2+1)=8

ln (x) + ln (x^{2} + 1) = 8