簡約 (7ln(2)-ln(12.8))/(ln(36.1)-ln(22))

解

簡約

\frac{7 ln ( 2 ) - ln ( 12.8 )}{ln ( 36.1 ) - ln ( 22 )}

\frac{ln ( 10 )}{ln ( 1.64090 \dots )}

十進法表記

4.64933 \dots

解答ステップ

\frac{7 ln ( 2 ) - ln ( 12.8 )}{ln ( 36.1 ) - ln ( 22 )}

対数の規則を適用する:

a lo g_{c} (b) = lo g_{c} (b^{a})

7 ln (2) = ln (2^{7})

= \frac{ln ( 2 ^{7} ) - ln ( 12.8 )}{ln ( 36.1 ) - ln ( 22 )}

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^{7}) - ln (12.8) = ln (\frac{2 ^{7}}{12.8})

= \frac{ln ( \frac{2 ^{7}}{12.8} )}{ln ( 36.1 ) - ln ( 22 )}

\frac{2 ^{7}}{12.8} = 10

= \frac{ln ( 10 )}{ln ( 36.1 ) - ln ( 22 )}

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 (36.1) - ln (22) = ln (\frac{36.1}{22})

= \frac{ln ( 10 )}{ln ( \frac{36.1}{22} )}

数を割る:

\frac{36.1}{22} = 1.64090 \dots

= \frac{ln ( 10 )}{ln ( 1.64090 \dots )}