簡約 ln((2^{0.538+1}-1)/((0.538-1)x))

解

簡約

ln (\frac{2 ^{0.538 + 1} - 1}{( 0.538 - 1 ) x})

ln (2^{1.538} - 1) - ln (- 0.462) - ln (x)

解答ステップ

ln (\frac{2 ^{0.538 + 1} - 1}{( 0.538 - 1 ) x})

対数の規則を適用する:

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

ln (\frac{2 ^{0.538 + 1} - 1}{( 0.538 - 1 ) x}) = ln (2^{0.538 + 1} - 1) - ln ((0.538 - 1) x)

= ln (2^{1 + 0.538} - 1) - ln ((0.538 - 1) x)

対数の規則を適用する:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

ln ((0.538 - 1) x) = ln (0.538 - 1) + ln (x)

= ln (2^{1 + 0.538} - 1) - (ln (x) + ln (0.538 - 1))

数を足す:

0.538 + 1 = 1.538

= ln (2^{1.538} - 1) - (ln (x) + ln (0.538 - 1))

数を引く:

0.538 - 1 = - 0.462

= ln (2^{1.538} - 1) - (ln (x) + ln (- 0.462))

- (ln (- 0.462) + ln (x)) : - ln (- 0.462) - ln (x)

= ln (2^{1.538} - 1) - ln (- 0.462) - ln (x)