展開する (log_{10}(x)(x^2+6)-1)/2

解

展開する

\frac{lo g _{10} ( x ) ( x ^{2} + 6 ) - 1}{2}

\frac{x ^{2} lo g _{10} ( x )}{2} + 3 lo g_{10} (x) - \frac{1}{2}

解答ステップ

\frac{lo g _{10} ( x ) ( x ^{2} + 6 ) - 1}{2}

拡張

lo g_{10} (x) (x^{2} + 6) - 1 : x^{2} lo g_{10} (x) + 6 lo g_{10} (x) - 1

= \frac{x ^{2} lo g _{10} ( x ) + 6 lo g _{10} ( x ) - 1}{2}

分数の規則を適用する:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{x ^{2} lo g _{10} ( x ) + 6 lo g _{10} ( x ) - 1}{2} = \frac{x ^{2} lo g _{10} ( x )}{2} + \frac{6 lo g _{10} ( x )}{2} - \frac{1}{2}

= \frac{x ^{2} lo g _{10} ( x )}{2} + \frac{6 lo g _{10} ( x )}{2} - \frac{1}{2}

数を割る:

\frac{6}{2} = 3

= \frac{x ^{2} lo g _{10} ( x )}{2} + 3 lo g_{10} (x) - \frac{1}{2}