What is 57/40+4/5 ln(5/4)-3/8 ln(2) ?

The solution to 57/40+4/5 ln(5/4)-3/8 ln(2) is 57/40+ln((\sqrt[40]{2}*5^{4/5})/(2^2))

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simplify 57/40+4/5 ln(5/4)-3/8 ln(2)

simplify

\frac{57}{40} + \frac{4}{5} ln (\frac{5}{4}) - \frac{3}{8} ln (2)

Decimal Notation

1.34358 \dots

Solution steps

\frac{57}{40} + \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{57}{40} + 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{57}{40} + 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} (\frac{a}{b})

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

= \frac{57}{40} + ln \frac{( \frac{5}{4} ) ^{\frac{4}{5}}}{2 ^{\frac{3}{8}}}

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d + θ ln (k) + γ ln (ω) - ln (\frac{1}{1 + βθ} k^{α} ω) - β d

6 lo g_{8} (u) + 6 lo g_{8} (w) - 36 lo g_{8} (v)

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What is 57/40+4/5 ln(5/4)-3/8 ln(2) ?
The solution to 57/40+4/5 ln(5/4)-3/8 ln(2) is 57/40+ln((\sqrt[40]{2}*5^{4/5})/(2^2))