化简 0.026ln(0.095)+0.416ln(10)

解答

化简

0.026 ln (0.095) + 0.416 ln (10)

ln (2.45143 \dots)

十进制

0.89667 \dots

求解步骤

0.026 ln (0.095) + 0.416 ln (10)

使用对数计算法则:

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

0.026 ln (0.095) = ln (0.09 5^{0.026})

= ln (0.09 5^{0.026}) + 0.416 ln (10)

使用对数计算法则:

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

0.416 ln (10) = ln (1 0^{0.416})

= ln (0.09 5^{0.026}) + ln (1 0^{0.416})

使用对数计算法则:

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

ln (0.09 5^{0.026}) + ln (1 0^{0.416}) = ln (1 0^{0.416} \cdot 0.09 5^{0.026})

= ln (1 0^{0.416} \cdot 0.09 5^{0.026})

0.09 5^{0.026} \cdot 1 0^{0.416} = 2.45143 \dots

= ln (2.45143 \dots)

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

s im pl i f y lo g_{2} (3) + 4 lo g_{2} (x) - 2 lo g_{2} (y)

s im pl i f y lo g_{10} (a) + 2 lo g_{10} (b) - 3 lo g_{10} (c)

e x p an d ln ((\frac{1}{x})^{\frac{1}{l n ( x )}})

j o in \frac{4 ln ( 2 )}{ln ( \frac{512}{3} )}