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受欢迎的代数 >

log_{10}(3x)=x-1

解答

lo g_{10} (3 x) = x - 1

解答

x = - \frac{W _{- 1} ( - \frac{l n ( 10 )}{30} )}{ln ( 10 )}, x = - \frac{W _{0} ( - \frac{l n ( 10 )}{30} )}{ln ( 10 )}

+1

十进制

x = 1.71015 \dots, x = 0.03623 \dots

求解步骤

lo g_{10} (3 x) = x - 1

若

f (x) = g (x)

，则

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

1 0^{l o g_{10} (3 x)} = 1 0^{x - 1}

化简

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

3 x = 1 0^{x - 1}

解

3 x = 1 0^{x - 1} : x = - \frac{W _{- 1} ( - \frac{l n ( 10 )}{30} )}{ln ( 10 )}, x = - \frac{W _{0} ( - \frac{l n ( 10 )}{30} )}{ln ( 10 )}

x = - \frac{W _{- 1} ( - \frac{l n ( 10 )}{30} )}{ln ( 10 )}, x = - \frac{W _{0} ( - \frac{l n ( 10 )}{30} )}{ln ( 10 )}

验证解:

x = - \frac{W _{- 1} ( - \frac{l n ( 10 )}{30} )}{ln ( 10 )}

真

, x = - \frac{W _{0} ( - \frac{l n ( 10 )}{30} )}{ln ( 10 )}

真

解为

x = - \frac{W _{- 1} ( - \frac{l n ( 10 )}{30} )}{ln ( 10 )}, x = - \frac{W _{0} ( - \frac{l n ( 10 )}{30} )}{ln ( 10 )}

作图

流行的例子

4ln(3x+5)-12=16

4 ln (3 x + 5) - 12 = 16

ln(2x+1)-1=ln(x-2)

ln (2 x + 1) - 1 = ln (x - 2)

-log_{10}(x)=3.9

- lo g_{10} (x) = 3.9

9× x^{log_{3}(x)}=x^3

9 \times x^{l o g_{3} (x)} = x^{3}

log_{10}(4x)-log_{10}(12+sqrt(x))=2

lo g_{10} (4 x) - lo g_{10} (12 + x) = 2