化简 97/100 ln(3*10^6)+3/100 ln(3000)

解答

化简

\frac{97}{100} ln (3 \cdot 1 0^{6}) + \frac{3}{100} ln (3000)

\frac{97}{100} ln (3) + \frac{291}{50} ln (10) + \frac{3}{100} ln (3000)

十进制

14.70689 \dots

求解步骤

\frac{97}{100} ln (3 \cdot 1 0^{6}) + \frac{3}{100} ln (3000)

使用对数计算法则:

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

\frac{97}{100} ln (3 \cdot 1 0^{6}) = \frac{97}{100} ln (3) + \frac{97}{100} ln (1 0^{6})

= \frac{97}{100} ln (3) + \frac{97}{100} ln (1 0^{6}) + \frac{3}{100} ln (3000)

使用对数计算法则:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln (1 0^{6}) = 6 ln (10)

= \frac{97}{100} ln (3) + \frac{97}{100} \cdot 6 ln (10) + \frac{3}{100} ln (3000)

\frac{97}{100} \cdot 6 ln (10) = \frac{291}{50} ln (10)

= \frac{97}{100} ln (3) + \frac{291}{50} ln (10) + \frac{3}{100} ln (3000)

j o in \frac{2 ln ( \frac{3 e ^{2}}{2} )}{e}

s im pl i f y 4 lo g_{b} (X) - lo g_{b} (y)

s im pl i f y lo g_{a} (\frac{x + y}{( x - y ) ^{3}})

d o main f (x) = \frac{1}{2} ln (5 x^{2}) - \frac{1}{2} ln (2 x^{2})

s im pl i f y - lo g_{10} (2.635 \cdot 1 0^{- 6})