簡約 (ln(2.99)-ln(3))/((2.99)-3)

解

簡約

\frac{ln ( 2.99 ) - ln ( 3 )}{( 2.99 ) - 3}

- \frac{ln ( 0.99666 \dots )}{0.01}

十進法表記

0.33389 \dots

解答ステップ

\frac{ln ( 2.99 ) - ln ( 3 )}{( 2.99 ) - 3}

対数の規則を適用する:

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

ln (2.99) - ln (3) = ln (\frac{2.99}{3})

= \frac{ln ( \frac{2.99}{3} )}{2.99 - 3}

数を割る:

\frac{2.99}{3} = 0.99666 \dots

= \frac{ln ( 0.99666 \dots )}{2.99 - 3}

数を引く:

2.99 - 3 = - 0.01

= \frac{ln ( 0.99666 \dots )}{- 0.01}

分数の規則を適用する:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{ln ( 0.99666 \dots )}{0.01}