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受欢迎的代数 >

(x)=log_{0.5}(x-2)+1

解答

(x) = lo g_{0.5} (x - 2) + 1

解答

x = - \frac{W _{0} ( - 0.5 ln ( 0.5 ) ) - 2 ln ( 0.5 )}{ln ( 0.5 )}

+1

十进制

x = 2.38333 \dots

求解步骤

(x) = lo g_{0.5} (x - 2) + 1

交换两边

lo g_{0.5} (x - 2) + 1 = x

将

1

到右边

lo g_{0.5} (x - 2) = x - 1

若

f (x) = g (x)

，则

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

0. 5^{l o g_{0.5} (x - 2)} = 0. 5^{x - 1}

化简

0. 5^{l o g_{0.5} (x - 2)} : x - 2

x - 2 = 0. 5^{x - 1}

解

x - 2 = 0. 5^{x - 1} : x = - \frac{W _{0} ( - 0.5 ln ( 0.5 ) ) - 2 ln ( 0.5 )}{ln ( 0.5 )}

x = - \frac{W _{0} ( - 0.5 ln ( 0.5 ) ) - 2 ln ( 0.5 )}{ln ( 0.5 )}

验证解:

x = - \frac{W _{0} ( - 0.5 ln ( 0.5 ) ) - 2 ln ( 0.5 )}{ln ( 0.5 )}

真

解是

x = - \frac{W _{0} ( - 0.5 ln ( 0.5 ) ) - 2 ln ( 0.5 )}{ln ( 0.5 )}

作图

流行的例子

log_{3}(5x-3)=5

lo g_{3} (5 x - 3) = 5

log_{2}(x+20)=log_{2}(2)

lo g_{2} (x + 20) = lo g_{2} (2)

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

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

7 lo g_{10} (u) = 1

ln (x^{2}) + 2 x - 5 = 0