What is 3/8*ln(8/3)+(5/16*ln(16/5))*2 ?

The solution to 3/8*ln(8/3)+(5/16*ln(16/5))*2 is 3/8 (3ln(2)-ln(3))+5/8 ln(16/5)

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simplify 3/8ln(8/3)+(5/16ln(16/5))*2

simplify

\frac{3}{8} \cdot ln (\frac{8}{3}) + (\frac{5}{16} \cdot ln (\frac{16}{5})) \cdot 2

\frac{3}{8} (3 ln (2) - ln (3)) + \frac{5}{8} ln (\frac{16}{5})

Decimal Notation

1.09478 \dots

Solution steps

\frac{3}{8} ln (\frac{8}{3}) + (\frac{5}{16} ln (\frac{16}{5})) \cdot 2

Apply log rule:

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

ln (\frac{8}{3}) = ln (8) - ln (3)

= \frac{3}{8} (ln (8) - ln (3)) + 2 \cdot \frac{5}{16} ln (\frac{16}{5})

\frac{3}{8} (ln (8) - ln (3)) = \frac{3}{8} (3 ln (2) - ln (3))

\frac{5}{16} ln (\frac{16}{5}) \cdot 2 = \frac{5}{8} ln (\frac{16}{5})

= \frac{3}{8} (3 ln (2) - ln (3)) + \frac{5}{8} ln (\frac{16}{5})

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What is 3/8*ln(8/3)+(5/16*ln(16/5))*2 ?
The solution to 3/8*ln(8/3)+(5/16*ln(16/5))*2 is 3/8 (3ln(2)-ln(3))+5/8 ln(16/5)