簡約 log_{2}(15)+6log_{2}(x)-4/3 log_{2}(x)-1/3 log_{2}(x+3)

解

簡約

lo g_{2} (15) + 6 lo g_{2} (x) - \frac{4}{3} lo g_{2} (x) - \frac{1}{3} lo g_{2} (x + 3)

lo g_{2} (15) + \frac{14 lo g _{2} ( x ) - lo g _{2} ( x + 3 )}{3}

解答ステップ

lo g_{2} (15) + 6 lo g_{2} (x) - \frac{4}{3} lo g_{2} (x) - \frac{1}{3} lo g_{2} (x + 3)

共通項をくくり出す

lo g_{2} (x)

= lo g_{2} (15) + lo g_{2} (x) (6 - \frac{4}{3}) - \frac{1}{3} lo g_{2} (x + 3)

6 - \frac{4}{3} = \frac{14}{3}

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

= lo g_{2} (15) + lo g_{2} (x) \frac{14}{3} - \frac{lo g _{2} ( x + 3 )}{3}

簡素化

lo g_{2} (x) \frac{14}{3} : \frac{lo g _{2} ( x ) \cdot 14}{3}

= lo g_{2} (15) + \frac{lo g _{2} ( x ) \cdot 14}{3} - \frac{lo g _{2} ( x + 3 )}{3}

結合

lo g_{2} (15) + \frac{lo g _{2} ( x ) \cdot 14}{3} - \frac{lo g _{2} ( x + 3 )}{3} : lo g_{2} (15) + \frac{lo g _{2} ( x ) \cdot 14 - lo g _{2} ( x + 3 )}{3}

= lo g_{2} (15) + \frac{lo g _{2} ( x ) \cdot 14 - lo g _{2} ( x + 3 )}{3}

= lo g_{2} (15) + \frac{14 lo g _{2} ( x ) - lo g _{2} ( x + 3 )}{3}