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

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

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

simplify

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

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

Decimal Notation

1.40600 \dots

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

lo g_{7} (\frac{1 + 2 e ^{- x}}{e ^{2 x}})

ln ((24 e^{- x - y})^{5}) + ln ((15 e^{3 x - y})^{3})

ln (\frac{0.85}{0.6108})

lo g_{3} ((6 x)^{2})

lo g_{10} (\frac{y ^{4} x ^{2}}{z})

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