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受欢迎的代数 >

13log_{10}(10x)=338-xlog_{10}(10)

解答

13 lo g_{10} (10 x) = 338 - x lo g_{10} (10)

解答

x = \frac{13 W _{0} ( \frac{l n ( 10 ) \cdot 1 0 ^{25}}{13} )}{ln ( 10 )}

+1

十进制

x = 292.93203 \dots

求解步骤

13 lo g_{10} (10 x) = 338 - x lo g_{10} (10)

两边除以

13

lo g_{10} (10 x) = \frac{338 - x lo g _{10} ( 10 )}{13}

使用对数运算法则

lo g_{10} (10 x) = \frac{338 - x}{13}

若

f (x) = g (x)

，则

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

1 0^{l o g_{10} (10 x)} = 1 0^{\frac{338 - x}{13}}

化简

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

10 x = 1 0^{\frac{338 - x}{13}}

解

10 x = 1 0^{\frac{338 - x}{13}} : x = \frac{13 W _{0} ( \frac{l n ( 10 ) \cdot 1 0 ^{25}}{13} )}{ln ( 10 )}

x = \frac{13 W _{0} ( \frac{l n ( 10 ) \cdot 1 0 ^{25}}{13} )}{ln ( 10 )}

验证解:

x = \frac{13 W _{0} ( \frac{l n ( 10 ) \cdot 1 0 ^{25}}{13} )}{ln ( 10 )}

真

解是

x = \frac{13 W _{0} ( \frac{l n ( 10 ) \cdot 1 0 ^{25}}{13} )}{ln ( 10 )}

作图

流行的例子

2 \cdot lo g_{2} (x) = 4

log_{2}(log_{3}(log_{3}(b)))=0

lo g_{2} (lo g_{3} (lo g_{3} (b))) = 0

ln (x + 4) = - 2

log_{10}(0.3x)=-2

lo g_{10} (0.3 x) = - 2

log_{3}(log_{10}(9x)+12+9^x)=2x

lo g_{3} (lo g_{10} (9 x) + 12 + 9^{x}) = 2 x