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受欢迎的代数 >

5000log_{10}(n)=n

解答

5000 lo g_{10} (n) = n

解答

n = - \frac{5000 W _{- 1} ( - \frac{l n ( 10 )}{5000} )}{ln ( 10 )}, n = - \frac{5000 W _{0} ( - \frac{l n ( 10 )}{5000} )}{ln ( 10 )}

+1

十进制

n = 21680.32937 \dots, n = 1.00046 \dots

求解步骤

5000 lo g_{10} (n) = n

两边除以

5000

lo g_{10} (n) = \frac{n}{5000}

若

f (x) = g (x)

，则

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

1 0^{l o g_{10} (n)} = 1 0^{\frac{n}{5000}}

化简

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

n = 1 0^{\frac{n}{5000}}

解

n = 1 0^{\frac{n}{5000}} : n = - \frac{5000 W _{- 1} ( - \frac{l n ( 10 )}{5000} )}{ln ( 10 )}, n = - \frac{5000 W _{0} ( - \frac{l n ( 10 )}{5000} )}{ln ( 10 )}

n = - \frac{5000 W _{- 1} ( - \frac{l n ( 10 )}{5000} )}{ln ( 10 )}, n = - \frac{5000 W _{0} ( - \frac{l n ( 10 )}{5000} )}{ln ( 10 )}

验证解:

n = - \frac{5000 W _{- 1} ( - \frac{l n ( 10 )}{5000} )}{ln ( 10 )}

真

, n = - \frac{5000 W _{0} ( - \frac{l n ( 10 )}{5000} )}{ln ( 10 )}

真

解为

n = - \frac{5000 W _{- 1} ( - \frac{l n ( 10 )}{5000} )}{ln ( 10 )}, n = - \frac{5000 W _{0} ( - \frac{l n ( 10 )}{5000} )}{ln ( 10 )}

作图

流行的例子

log_{2}((r+18)^2)=6

lo g_{2} ((r + 18)^{2}) = 6

log_{10}(2x+1)=log_{10}(3x)

lo g_{10} (2 x + 1) = lo g_{10} (3 x)

x^{log_{3}(x)}=9x^{-1}

x^{l o g_{3} (x)} = 9 x^{- 1}

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

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

15=6log_{4}(8x)

15 = 6 lo g_{4} (8 x)