簡約 3/4*log_{2}(((3/4))/((1/20)))

解

簡約

\frac{3}{4} \cdot lo g_{2} (\frac{( \frac{3}{4} )}{( \frac{1}{20} )})

\frac{3}{4} (lo g_{2} (\frac{3}{4}) + lo g_{2} (20))

十進法表記

2.93016 \dots

解答ステップ

\frac{3}{4} lo g_{2} (\frac{( \frac{3}{4} )}{( \frac{1}{20} )})

対数の規則を適用する:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

lo g_{2} (\frac{( \frac{3}{4} )}{( \frac{1}{20} )}) = lo g_{2} ((\frac{3}{4})) - lo g_{2} ((\frac{1}{20}))

= \frac{3}{4} (lo g_{2} (\frac{3}{4}) - lo g_{2} (\frac{1}{20}))

対数の規則を適用する:

lo g_{a} (\frac{1}{x}) = - lo g_{a} (x)

= \frac{3}{4} (lo g_{2} (\frac{3}{4}) - (- lo g_{2} (20)))

規則を適用

- (- a) = a

= \frac{3}{4} (lo g_{2} (\frac{3}{4}) + lo g_{2} (20))