What is 19/13+4/5 ln(5/4)+3/8 ln(2) ?

The solution to 19/13+4/5 ln(5/4)+3/8 ln(2) is 19/13+ln((5/4)^{4/5}*2^{3/8})

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simplify 19/13+4/5 ln(5/4)+3/8 ln(2)

simplify

\frac{19}{13} + \frac{4}{5} ln (\frac{5}{4}) + \frac{3}{8} ln (2)

\frac{19}{13} + ln ((\frac{5}{4})^{\frac{4}{5}} \cdot 2^{\frac{3}{8}})

Decimal

1.89998 \dots

Solution steps

\frac{19}{13} + \frac{4}{5} ln (\frac{5}{4}) + \frac{3}{8} ln (2)

Apply log rule:

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

\frac{4}{5} ln (\frac{5}{4}) = ln ((\frac{5}{4})^{\frac{4}{5}})

= \frac{19}{13} + ln ((\frac{5}{4})^{\frac{4}{5}}) + \frac{3}{8} ln (2)

Apply log rule:

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

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

= \frac{19}{13} + ln ((\frac{5}{4})^{\frac{4}{5}}) + ln (2^{\frac{3}{8}})

Apply log rule:

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

ln ((\frac{5}{4})^{\frac{4}{5}}) + ln (2^{\frac{3}{8}}) = ln (2^{\frac{3}{8}} (\frac{5}{4})^{\frac{4}{5}})

= \frac{19}{13} + ln ((\frac{5}{4})^{\frac{4}{5}} \cdot 2^{\frac{3}{8}})

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What is 19/13+4/5 ln(5/4)+3/8 ln(2) ?
The solution to 19/13+4/5 ln(5/4)+3/8 ln(2) is 19/13+ln((5/4)^{4/5}*2^{3/8})