What is 7/4*ln(7/4)-1/(7/4) ?

The solution to 7/4*ln(7/4)-1/(7/4) is 7/4 (ln(7)-2ln(2))-4/7

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simplify 7/4*ln(7/4)-1/(7/4)

simplify

\frac{7}{4} \cdot ln (\frac{7}{4}) - \frac{1}{\frac{7}{4}}

\frac{7}{4} (ln (7) - 2 ln (2)) - \frac{4}{7}

Decimal

0.40789 \dots

Solution steps

\frac{7}{4} ln (\frac{7}{4}) - \frac{1}{\frac{7}{4}}

Apply log rule:

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

ln (\frac{7}{4}) = ln (7) - ln (4)

= \frac{7}{4} (ln (7) - ln (4)) - \frac{1}{\frac{7}{4}}

ln (4) = 2 ln (2)

= \frac{7}{4} (ln (7) - 2 ln (2)) - \frac{1}{\frac{7}{4}}

Apply the fraction rule:

\frac{1}{\frac{b}{c}} = \frac{c}{b}

= \frac{7}{4} (ln (7) - 2 ln (2)) - \frac{4}{7}

- ln (4) + ln (\frac{1}{4})

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3 lo g_{5} (x + 2) - lo g_{5} (x)

ln (6 + x) - ln (x)

What is 7/4*ln(7/4)-1/(7/4) ?
The solution to 7/4*ln(7/4)-1/(7/4) is 7/4 (ln(7)-2ln(2))-4/7