化简 ((1+log_{2}(x-4)))/((log_{sqrt(2))(sqrt(x+3)-sqrt(x-3)))}

解答

化简

\frac{( 1 + lo g _{2} ( x - 4 ) )}{( lo g _{2} ( x + 3 - x - 3 ) )}

\frac{1 + lo g _{2} ( x - 4 )}{2 lo g _{2} ( x + 3 - x - 3 )}

求解步骤

\frac{1 + lo g _{2} ( x - 4 )}{lo g _{2} ( x + 3 - x - 3 )}

使用根式运算法则:

a = a^{\frac{1}{2}}

2 = 2^{\frac{1}{2}}

= \frac{1 + lo g _{2} ( x - 4 )}{lo g _{2^{\frac{1}{2}}} ( x + 3 - x - 3 )}

使用对数计算法则:

lo g_{a^{b}} (x) = \frac{1}{b} lo g_{a} (x), a > 0

lo g_{2^{\frac{1}{2}}} (x + 3 - x - 3) = \frac{1}{\frac{1}{2}} lo g_{2} (x + 3 - x - 3)

= \frac{1 + lo g _{2} ( x - 4 )}{\frac{1}{\frac{1}{2}} lo g _{2} ( x + 3 - x - 3 )}

\frac{1}{\frac{1}{2}} = 2

= \frac{1 + lo g _{2} ( x - 4 )}{2 lo g _{2} ( x + 3 - x - 3 )}

f a c t or 81 a^{4} b^{4} - 256

f a c t or 1.5 x^{4} - 3 x^{3}

s im pl i f y 4 \frac{x ^{2}}{25} y^{2} + \frac{1}{5} + \frac{y ^{2}}{16} x^{2}

e x p an d (x^{4} - 2 x^{2})^{2} - 1

s im pl i f y 1863 - 220603 - 48575 k