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 97/100ln(310^6)+3/100*ln(3000)

simplify

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

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

Decimal Notation

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)

e^{\frac{l n ( 3 ) + l n ( 5 )}{2}}

7 lo g_{m} (z) - \frac{1}{2} lo g_{m} (w) + 5 lo g_{m} (x)

0 ln (\frac{\frac{20000}{17} - 1}{1199})

lo g_{e} (\frac{e ^{2} - 2 e ^{a + 2 b}}{1 - 2 e ^{a + 2 b}})

10 ln (\frac{47}{4})

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)