化简 (43pi)/(10)+ln(7)-1/2*ln(26)-169760

解答

化简

\frac{43 π}{10} + ln (7) - \frac{1}{2} \cdot ln (26) - 169760

\frac{43 π}{10} + ln (\frac{7 26}{26}) - 169760

十进制

- 169746.17428 \dots

求解步骤

\frac{43 π}{10} + ln (7) - \frac{1}{2} ln (26) - 169760

使用对数计算法则:

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

\frac{1}{2} ln (26) = ln (2 6^{\frac{1}{2}})

= \frac{43 π}{10} + ln (7) - ln (2 6^{\frac{1}{2}}) - 169760

使用对数计算法则:

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

ln (7) - ln (2 6^{\frac{1}{2}}) = ln (\frac{7}{2 6 ^{\frac{1}{2}}})

= \frac{43 π}{10} + ln (\frac{7}{2 6 ^{\frac{1}{2}}}) - 169760

\frac{7}{2 6 ^{\frac{1}{2}}} = \frac{7 26}{26}

= \frac{43 π}{10} + ln (\frac{7 26}{26}) - 169760

s im pl i f y ln (\frac{2 x}{e ^{2 x}})

s im pl i f y \frac{1}{2} ln (x - 3) + \frac{1}{2} ln (x + 3) - ln (x)

s im pl i f y 4.74 + lo g_{10} (\frac{50}{10})

e x p an d lo g_{2} ((x^{3} + 2) 4 (x - 4)^{5})

s im pl i f y \frac{( ln ∣ x + 4 ∣ - 6 ln ∣ x - 1 ∣ )}{5}