What is 97/100 ln(3*10^6)+3/100 ln(3000) ?

The solution to 97/100 ln(3*10^6)+3/100 ln(3000) is 97/100 ln(3)+291/50 ln(10)+3/100 ln(3000)

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simplify 97/100 ln(3*10^6)+3/100 ln(3000)

simplify

\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)

Decimal

14.70689 \dots

Solution steps

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

Apply log rule:

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)

Apply log rule:

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)

What is 97/100 ln(3*10^6)+3/100 ln(3000) ?
The solution to 97/100 ln(3*10^6)+3/100 ln(3000) is 97/100 ln(3)+291/50 ln(10)+3/100 ln(3000)