展开 (log_{10}(x)(x^2+6)-1)/2

解答

展开

\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}

求解步骤

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

乘开

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}

使用分式法则:

\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}

数字相除:

\frac{6}{2} = 3

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

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