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受欢迎的代数 >

2log_{10}(x+3)=2x+3

解答

2 lo g_{10} (x + 3) = 2 x + 3

解答

x = - \frac{W _{- 1} ( - \frac{l n ( 10 )}{e ^{\frac{3 l n ( 10 )}{2}}} ) + 3 ln ( 10 )}{ln ( 10 )}, x = - \frac{W _{0} ( - \frac{l n ( 10 )}{e ^{\frac{3 l n ( 10 )}{2}}} ) + 3 ln ( 10 )}{ln ( 10 )}

+1

十进制

x = - 1.25926 \dots, x = - 2.96578 \dots

求解步骤

2 lo g_{10} (x + 3) = 2 x + 3

两边除以

2

lo g_{10} (x + 3) = \frac{2 x + 3}{2}

若

f (x) = g (x)

，则

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

1 0^{l o g_{10} (x + 3)} = 1 0^{\frac{2 x + 3}{2}}

化简

1 0^{l o g_{10} (x + 3)} : x + 3

x + 3 = 1 0^{\frac{2 x + 3}{2}}

解

x + 3 = 1 0^{\frac{2 x + 3}{2}} : x = - \frac{W _{- 1} ( - \frac{l n ( 10 )}{e ^{\frac{3 l n ( 10 )}{2}}} ) + 3 ln ( 10 )}{ln ( 10 )}, x = - \frac{W _{0} ( - \frac{l n ( 10 )}{e ^{\frac{3 l n ( 10 )}{2}}} ) + 3 ln ( 10 )}{ln ( 10 )}

x = - \frac{W _{- 1} ( - \frac{l n ( 10 )}{e ^{\frac{3 l n ( 10 )}{2}}} ) + 3 ln ( 10 )}{ln ( 10 )}, x = - \frac{W _{0} ( - \frac{l n ( 10 )}{e ^{\frac{3 l n ( 10 )}{2}}} ) + 3 ln ( 10 )}{ln ( 10 )}

验证解:

x = - \frac{W _{- 1} ( - \frac{l n ( 10 )}{e ^{\frac{3 l n ( 10 )}{2}}} ) + 3 ln ( 10 )}{ln ( 10 )}

真

, x = - \frac{W _{0} ( - \frac{l n ( 10 )}{e ^{\frac{3 l n ( 10 )}{2}}} ) + 3 ln ( 10 )}{ln ( 10 )}

真

解为

x = - \frac{W _{- 1} ( - \frac{l n ( 10 )}{e ^{\frac{3 l n ( 10 )}{2}}} ) + 3 ln ( 10 )}{ln ( 10 )}, x = - \frac{W _{0} ( - \frac{l n ( 10 )}{e ^{\frac{3 l n ( 10 )}{2}}} ) + 3 ln ( 10 )}{ln ( 10 )}

作图

流行的例子

log_{10}(x)+log_{10}(x+4)=-1

lo g_{10} (x) + lo g_{10} (x + 4) = - 1

log_{125}(x)-log_{5}(x)=-2

lo g_{125} (x) - lo g_{5} (x) = - 2

20*log_{10}(x)=100

20 \cdot lo g_{10} (x) = 100

log_{2}(x)*log_{2}(x)=9

lo g_{2} (x) \cdot lo g_{2} (x) = 9

lo g_{x} (121) = 2