簡約 (((ln(1.01)-ln(0.99))))/(0.02)

解

簡約

\frac{( ( ln ( 1.01 ) - ln ( 0.99 ) ) )}{0.02}

\frac{ln ( 1.02020 \dots )}{0.02}

十進法表記

1.00003 \dots

解答ステップ

\frac{( ( ln ( 1.01 ) - ln ( 0.99 ) ) )}{0.02}

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 (1.01) - ln (0.99) = ln (\frac{1.01}{0.99})

= \frac{ln ( \frac{1.01}{0.99} )}{0.02}

数を割る:

\frac{1.01}{0.99} = 1.02020 \dots

= \frac{ln ( 1.02020 \dots )}{0.02}